Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic284 |
| Sylow | C71 ⋊ C23×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D284 |
| commutator | C4×C71 | C25 |
| Frattini | C4 | C24×D71 |
| Fitting | C23×C8×C71 | C2 |
| socle | C24×C71 | D4 |
| hypercenter | C23×C8 | D71 |
| hypocenter | C71 | C23×Q16 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1464 conjugacy classes of subgroups.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31904262, #31904264, #31904288, … |
| maximal normal subgroup of | #31904262, #31904264, #31904288, … |
| maximal quotient of | C23×#14556053, C23×#14556062, C22×C4×Dic284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 19233);