Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
| direct product | C4×#14556038 |
| Sylow | C71 ⋊ C4×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×D71 |
| commutator | C2×C71 | C43 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | C2×C4×C8×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C2×C4×C8 | D71 |
| hypocenter | C71 | C4×#97 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C42 ◁ C2×C4×C8 | |
360 conjugacy classes of subgroups.
2320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31884309, C8×#14556038, #31886804, … |
| maximal normal subgroup of | #31884309, C8×#14556038, #31886804, … |
| maximal quotient of | C4×#17985720, C4×#17985721, C8×#14556038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4194);