Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×#125×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3512 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D71 |
| commutator, socle | C22×C71 | C25 |
| Fitting | C2×#125×C71 | C2 |
| hypercenter | C2×#125 | D71 |
| hypocenter | C71 | #3512 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×#125 | |
1032 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|b^2=g,c^2=fg,d^2=f,e^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^70,d^b=df,h^b=h^701024 conjugacy classes — view the full character table.
| maximal subgroup of | #31889706, #31965685, #31965691, … |
| maximal normal subgroup of | #31889706, #31965685, #31965691, … |
| maximal quotient of | #32157606, #32157836, #32157933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 18434);