Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | C16×Dic142 |
| Sylow | C71 ⋊ Q8×C16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16 | C2×D71 |
| commutator | C2×C71 | C22×C16 |
| Frattini | C2×C8 | C22×D71 |
| Fitting | C4×C16×C71 | C2 |
| socle | C22×C71 | C22×C8 |
| hypercenter | C4×C16 | D71 |
| hypocenter | C71 | Q8×C16 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C16 ◁ C4×C16 | |
134 conjugacy classes of subgroups.
2320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31884928, #31884930, C16×#11765853, … |
| maximal normal subgroup of | #31884928, #31884930, C16×#11765853, … |
| maximal quotient of | C16×C4⋊Dic71, C16×Dic71⋊C4, #31915066, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6413);