Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#17986764 |
| Fitting | C2×#131×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#568 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D71 |
| commutator | C2×C71 | C24×C4 |
| Frattini | C4 | C24×D71 |
| Fitting | C2×#131×C71 | C2 |
| socle | C22×C71 | C23×C4 |
| hypercenter | C2×#131 | D71 |
| hypocenter | C71 | C2×#568 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#131 | |
1460 conjugacy classes of subgroups.
1468 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31912907, #31995154, #31995303, … |
| maximal normal subgroup of | #31912907, #31995154, #31995303, … |
| maximal quotient of | C2×#22596756, C2×#22596766, C2×#22596767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 19218);