Finite Group DatabasebetaFinite Group Databasebeta| order | 8526 |
| isoclinism | isoclinic class of #64425 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C7 |
| direct product | C29×#64425 |
| Fitting, socle, Hall | C72×C29 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C3×C29 |
| Hall | C29×#3862 ⋊ C2 |
| Hall | C29×C7⋊D7 ⋊ C3 |
| Hall | #3862 ⋊ C2×C29 |
| Hall | C7⋊D7 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #64425 |
| commutator, hypocenter | C72 | C2×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C72×C29 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C29 | |
40 conjugacy classes of subgroups.
406 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#64425, C29×#64422⋊C2, #30684931, … |
| maximal normal subgroup of | D29×#64425, C29×#64422⋊C2, #30684931, … |
| maximal quotient of | C29×#10596875, C2×C29×#64425, C29×#11725078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8526, 35);