Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #542×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3521 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D71 |
| commutator, socle | C22×C71 | C25 |
| Fitting | #542×C71 | C2 |
| hypercenter | #542 | D71 |
| hypocenter | C71 | #3521 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #542 | |
1042 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|c^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^70,h^c=h^70,h^d=h^70814 conjugacy classes — view the full character table.
| maximal subgroup of | #32880138, #32880154, #32880165, … |
| maximal normal subgroup of | #32880138, #32880154, #32880165, … |
| maximal quotient of | #32157680, #32158187, #32158226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 18576);