Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#17985774 |
| Sylow | C71 ⋊ C2×#346 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D71 |
| commutator | C2×C71 | C2×C4×C8 |
| Frattini | C2×C8 | C22×D71 |
| Fitting | C22×C16×C71 | C2 |
| socle | C23×C71 | C2×C8 |
| hypercenter | C22×C16 | D71 |
| hypocenter | C71 | C2×#346 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C8 ◁ C22×C16 | |
200 conjugacy classes of subgroups.
2320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31885140, #31885144, #346×Dic71, … |
| maximal normal subgroup of | #31885140, #31885144, #346×Dic71, … |
| maximal quotient of | C2×#22586256, C2×#22586259, #31906471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6099);