Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #400×D71 |
| Fitting | #400×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#400 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #400×C71 | C2 |
| hypercenter | #400 | D71 |
| hypocenter | C71 | C2×#400 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #400 | |
604 conjugacy classes of subgroups.
814 conjugacy classes — view the full character table.
| maximal subgroup of | #1353×D71, #31908184, #1615×D71, … |
| maximal normal subgroup of | #1353×D71, #31908184, #1615×D71, … |
| maximal quotient of | #1441×D71, #1442×D71, #1443×D71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7760);