Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | #418×D71 |
| Fitting | #418×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#418 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D71 |
| commutator | C4×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #418×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #418 | D71 |
| hypocenter | C71 | C2×#418 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #418 | |
1008 conjugacy classes of subgroups.
814 conjugacy classes — view the full character table.
| maximal subgroup of | #1795×D71, #1883×D71, #31998980, … |
| maximal normal subgroup of | #1795×D71, #1883×D71, #31998980, … |
| maximal quotient of | #1478×D71, #1490×D71, #31963890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13008);