Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #546×D71 |
| Fitting | #546×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#546 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D71 |
| commutator, socle | C22×C71 | C25 |
| Fitting | #546×C71 | C2 |
| hypercenter | #546 | D71 |
| hypocenter | C71 | C2×#546 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #546 | |
1900 conjugacy classes of subgroups.
925 conjugacy classes — view the full character table.
| maximal subgroup of | #3264×D71, #3266×D71, #3267×D71, … |
| maximal normal subgroup of | #3264×D71, #3266×D71, #3267×D71, … |
| maximal quotient of | D4×C22⋊C4×D71, #2339×D71, #2342×D71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17951);