Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C82×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1454 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D71 |
| commutator, socle | C22×C71 | C2×C42 |
| Fitting | C82×C71 | C2 |
| hypercenter | C82 | D71 |
| hypocenter | C71 | #1454 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C42 ◁ C82 | |
178 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cfg,c^b=cf,h^c=h^702296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1454×D71, C2×#22586639, #31963084, … |
| maximal normal subgroup of | #1454×D71, C2×#22586639, #31963084, … |
| maximal quotient of | #31886824, #31886842, #31887886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2809);