Finite Group DatabasebetaFinite Group Databasebeta| order | 8526 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D7×C29 |
| Fitting, socle, Hall | C3×C72×C29 ⋊ C2 |
| derived | C7 ⋊ C2×C3×C7×C29 |
| Hall | C72×C29 ⋊ C2×C3 |
| Hall | C3×C72 ⋊ C2×C29 |
| Sylow | C72 ⋊ C2×C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C29 | D7 |
| commutator, hypocenter | C7 | C2×C3×C7×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C29 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C7×C29 | |
44 conjugacy classes of subgroups.
3045 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D7×D29, C3×D72×C29, C3×D7×D203, … |
| maximal normal subgroup of | C3×C7×D7×D29, C3×D72×C29, C3×D7×D203, … |
| maximal quotient of | C3×C7×Dic7×C29, C2×C3×C7×D7×C29, C7×C9×D7×C29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8526, 53);