Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#17985756 |
| Sylow | C71 ⋊ C2×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic71 |
| commutator | C4×C71 | C2×C42 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | C22×M16×C71 | C2 |
| socle | C22×C71 | #95 |
| hypercenter | C22×M16 | D71 |
| hypocenter | C71 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C22×M16 | |
404 conjugacy classes of subgroups.
1444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31884583, #31884585, #31884589, … |
| maximal normal subgroup of | #31884583, #31884585, #31884589, … |
| maximal quotient of | C2×#22586168, #31886850, #31886853, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4211);