Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#123×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2457 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | C2×#123×C71 | C2 |
| hypercenter | C2×#123 | D71 |
| hypocenter | C71 | #2457 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
596 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|b^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^701018 conjugacy classes — view the full character table.
| maximal subgroup of | #2457×D71, C2×#22592243, #32165628, … |
| maximal normal subgroup of | #2457×D71, C2×#22592243, #32165628, … |
| maximal quotient of | #31919504, #31919742, #31920411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 8413);