Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C43 |
No aliases for this group.
| Fitting | C2×#127×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2867 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | C2×#127×C71 | C2 |
| hypercenter | C2×#127 | D71 |
| hypocenter | C71 | #2867 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
1272 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|b^2=e,c^2=f,d^2=g,b^a=be,c^a=cf,d^a=dg,h^d=h^701024 conjugacy classes — view the full character table.
| maximal subgroup of | #31896497, #31896548, #31900079, … |
| maximal normal subgroup of | #31896497, #31896548, #31900079, … |
| maximal quotient of | #31928657, #31928816, #31928817, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 12904);