Finite Group DatabasebetaFinite Group Databasebeta| order | 8526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊#64422 |
| Fitting, socle, derived, Hall | C72×C29 ⋊ C2×C3 |
| Hall | C29×#3862 ⋊ C2 |
| Hall | C7×D203 ⋊ C3 |
| Hall | #3862 ⋊ D29 |
| Sylow | C72 ⋊ C3×D29 |
| Sylow | C29 ⋊ #64422 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C29 | C2×C3 |
| LCS | G ▷ C72×C29 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,29|c^a=c^6,e^a=e^28,c^b=c^2,d^b=d^4283 conjugacy classes — view the full character table.
| maximal subgroup of | #64422⋊D29, #30684931, D29×#64422, … |
| maximal normal subgroup of | #64422⋊D29, #30684931, D29×#64422, … |
| maximal quotient of | #30684868, C2×C29⋊#64422, C29⋊#11725075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8526, 40);