Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#14556111 |
| Fitting | C22×C42×C71 ⋊ C2 |
| Sylow | C71 ⋊ C4×#123 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator | C22×C71 | C23×C4 |
| Frattini | C23 | C23×D71 |
| Fitting | C22×C42×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C22×C42 | D71 |
| hypocenter | C71 | C4×#123 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 | |
688 conjugacy classes of subgroups.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31892139, #31892149, C4×#17986188, … |
| maximal normal subgroup of | #31892139, #31892149, C4×#17986188, … |
| maximal quotient of | C4×#17985878, C4×#17985890, C4×#17985872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7032);