Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×Dic71 |
| Sylow | C71 ⋊ C22×C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D71 |
| commutator | C2×C71 | C24×C4 |
| Frattini | C22 | C24×D71 |
| Fitting | C23×Q8×C71 | C2 |
| socle | C24×C71 | C23 |
| hypercenter | C23×Q8 | D71 |
| hypocenter | C71 | C22×C4×Q8 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
1664 conjugacy classes of subgroups.
1480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31902880, #31903021, #391×Dic71, … |
| maximal normal subgroup of | #31902880, #31903021, #391×Dic71, … |
| maximal quotient of | C22×C4⋊C4×Dic71, C2×C4×Q8×Dic71, C22×#17985885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17686);