Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #576×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3584 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D71 |
| commutator | C4×C71 | C25 |
| Frattini | C4 | C24×D71 |
| Fitting | #576×C71 | C2 |
| socle | C2×C71 | C23×D4 |
| hypercenter | #576 | D71 |
| hypocenter | C71 | #3584 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #576 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,d^c=dg,h^e=h^70814 conjugacy classes — view the full character table.
| maximal subgroup of | #32151403, #32151409, #32151432, … |
| maximal normal subgroup of | #32151403, #32151409, #32151432, … |
| maximal quotient of | #32861012, #32861129, #32861565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 19278);