Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C71 ⋊ #2716 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #397×C71 | C2 |
| hypercenter | #397 | D71 |
| hypocenter | C71 | #2716 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #397 | |
450 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=e,b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^70,c^b=cg,d^b=de,h^b=h^70,h^c=h^70,h^d=h^70802 conjugacy classes — view the full character table.
| maximal subgroup of | #32204904, #32204906, #32204979, … |
| maximal normal subgroup of | #32204904, #32204906, #32204979, … |
| maximal quotient of | #31925068, #31925216, #31925534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 11343);