Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D4×#11765866 |
| Fitting | D4×Q8×C71 ⋊ C2 |
| Sylow | C71 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D71 |
| commutator, socle | C22×C71 | C25 |
| Fitting | D4×Q8×C71 | C2 |
| hypercenter | D4×Q8 | D71 |
| hypocenter | C71 | D4×#41 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1648 conjugacy classes of subgroups.
925 conjugacy classes — view the full character table.
| maximal subgroup of | #31973401, #31973409, #31973416, … |
| maximal normal subgroup of | #31973401, #31973409, #31973416, … |
| maximal quotient of | C22⋊C4×#11765866, C4⋊C4×#11765866, D4×#14556086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 18002);