Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #380×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2708 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #380×C71 | C2 |
| hypercenter | #380 | D71 |
| hypocenter | C71 | #2708 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #380 | |
568 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|c^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^70,h^d=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #32204809, #32204817, #32204940, … |
| maximal normal subgroup of | #32204809, #32204817, #32204940, … |
| maximal quotient of | #31924983, #31925116, #31925222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 11225);