Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #518×C71 ⋊ C2 |
| Sylow | C71 ⋊ C4×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D71 |
| commutator | C2×C71 | C24×C4 |
| Fitting | #518×C71 | C2 |
| socle | C22×C71 | C25 |
| hypercenter | #518 | D71 |
| hypocenter | C71 | C4×H(5,𝔽2) |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #518 | |
1660 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=g,e^2=g,b^a=bf,d^a=df,c^b=cf,h^e=h^701258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32003325, #32003331, #32003336, … |
| maximal normal subgroup of | #32003325, #32003331, #32003336, … |
| maximal quotient of | #32155682, #32155686, #518×Dic71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17714);