P1 x Fl(1,3,5) – Fano fourfolds

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
4-304-66-a	$(E^{ω_{4}})^{\oplus 2} \oplus E^{ω_{5}} \oplus E^{ω_{1} + ω_{2}}$ 2 copies of E^(w4) + E^(w5) + E^(w1 + w2)	4	7	66	304	6
3-272-60-d	$E^{ω_{2}} \oplus E^{2 ω_{5}} \oplus E^{ω_{1} + ω_{2}}$ E^(w2) + E^(2w5) + E^(w1 + w2)	3	4	60	272	4
3-141-35-b	$E^{ω_{4}} \oplus E^{ω_{5}} \oplus E^{ω_{2} + ω_{4}} \oplus E^{ω_{1} + ω_{2}}$ E^(w4) + E^(w5) + E^(w2 + w4) + E^(w1 + w2)	3	13	35	141	-11
3-162-39-f	$E^{ω_{2}} \oplus (E^{ω_{4}})^{\oplus 3} \oplus E^{ω_{1} + ω_{2}}$ E^(w2) + 3 copies of E^(w4) + E^(w1 + w2)	3	8	39	162	-5
3-225-51-c	$(E^{ω_{3}})^{\oplus 2} \oplus E^{ω_{1} + ω_{4}}$ 2 copies of E^(w3) + E^(w1 + w4)	3	9	51	225	-3
3-163-39-a	$E^{ω_{5}} \oplus E^{ω_{2} + ω_{5}} \oplus E^{ω_{1} + ω_{4}}$ E^(w5) + E^(w2 + w5) + E^(w1 + w4)	3	9	39	163	-5
3-188-44-d	$E^{ω_{3}} \oplus (E^{ω_{4}})^{\oplus 2} \oplus E^{ω_{1} + ω_{2}}$ E^(w3) + 2 copies of E^(w4) + E^(w1 + w2)	3	9	44	188	-5
4-125-32-b	$(E^{ω_{4}})^{\oplus 2} \oplus E^{ω_{5}} \oplus E^{ω_{1} + 2 ω_{2}}$ 2 copies of E^(w4) + E^(w5) + E^(w1 + 2w2)	4	18	32	125	-14
3-152-37-a	$E^{ω_{4}} \oplus E^{ω_{5}} \oplus E^{2 ω_{2}} \oplus E^{ω_{1} + ω_{4}}$ E^(w4) + E^(w5) + E^(2w2) + E^(w1 + w4)	3	8	37	152	-5

Fano fourfolds of type A beta