Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D3×D29 |
| unambiguous semidirect product | (D3×C29)⋊(C2×C52) |
| unambiguous semidirect product | (C3×D29)⋊(C2×C52) |
| unambiguous semidirect product | D87⋊(C2×C52) |
| Fitting, socle, Hall | C3×C52×C29 ⋊ C22 |
| derived, Hall | C3×C29 ⋊ C22×C52 |
| Hall | C52×C29 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C52×D3 |
| Sylow | C3 ⋊ C2×C52×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D3×D29 |
| commutator, hypocenter | C3×C29 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C29 | C22 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C52 | |
160 conjugacy classes of subgroups.
1200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D9×D29, D3×D29×C52⋊C3, C3×C52×D3×D29, … |
| maximal normal subgroup of | D3×D29×C52⋊C3, C3×C52×D3×D29 |
| maximal quotient of | C52×D9×D29, C3×C52×D3×D29, C52×D3×D87, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 100);