Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×C8×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2966 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D71 |
| commutator, socle | C22×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | C2×C4×C8×C71 | C2 |
| hypercenter | C2×C4×C8 | D71 |
| hypocenter | C71 | #2966 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C4×C8 | |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,d^a=dg,h^a=h^702296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31888491, #31888493, #31888498, … |
| maximal normal subgroup of | #31888491, #31888493, #31888498, … |
| maximal quotient of | #31995680, #31995700, #31995775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13485);