Finite Group DatabasebetaFinite Group Databasebeta| order | 8526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊#64418 |
| Fitting, socle, Hall | C72×C29 ⋊ D3 |
| derived, Hall | C29×#3862 ⋊ C2 |
| Hall | #3862 ⋊ D29 |
| Sylow | C72 ⋊ D87 |
| Sylow | C29 ⋊ #64418 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C29×#3862 | C2 |
| Fitting, socle | C72×C29 | D3 |
| LCS | G ▷ C29×#3862 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29,7^2|b^a=b^2,c^a=c^28,d^a=d^2e^3,e^a=d^6e^5,d^b=d^4e^4,e^b=e^2286 conjugacy classes — view the full character table.
| maximal subgroup of | #64418⋊D29, #30684948, D29×#64418, … |
| maximal normal subgroup of | #64418⋊D29, #30684948, D29×#64418, … |
| maximal quotient of | #30684876, C2×C29⋊#64418, C29⋊#11725071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8526, 48);