Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C71 ⋊ #2331 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | #391×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | #391 | D71 |
| hypocenter | C71 | #2331 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #391 | |
460 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=g,b^2=fg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^d=h^701024 conjugacy classes — view the full character table.
| maximal subgroup of | #2331×D71, C2×#22591083, #32156293, … |
| maximal normal subgroup of | #2331×D71, C2×#22591083, #32156293, … |
| maximal quotient of | #31918710, #31918738, #31918742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7253);