Finite Group DatabasebetaFinite Group Databasebeta| order | 8526 |
| isoclinism | isoclinic class of D87 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D87 |
| unambiguous semidirect product | C3⋊(C72×D29) |
| Fitting, socle, Hall | C3×C72×C29 ⋊ C2 |
| derived, Hall | C3×C29 ⋊ C2×C72 |
| Hall | C72×C29 ⋊ D3 |
| Hall | C3×C72 ⋊ D29 |
| Sylow | C29 ⋊ D3×C72 |
| Sylow | C3 ⋊ C72×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D87 |
| commutator, hypocenter | C3×C29 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C29 | C2 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C72 | |
80 conjugacy classes of subgroups.
2205 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C72×D29, C7×D7×D87, C7×D21⋊D29, … |
| maximal normal subgroup of | D3×C72×D29, C7×D7×D87, C7×D21⋊D29, … |
| maximal quotient of | C72×Dic87, C2×C72×D87, C72×D261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8526, 58);