Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D435 |
| unambiguous semidirect product | (C3×D5)⋊D145 |
| unambiguous semidirect product | (C5×D5)⋊D87 |
| unambiguous semidirect product | (D5×C29)⋊D15 |
| Fitting, socle, derived, Hall | C3×C52×C29 ⋊ C22 |
| Hall | C52×C29 ⋊ C2×D3 |
| Hall | C3×C29 ⋊ D52 |
| Hall | C3×C52 ⋊ C2×D29 |
| Sylow | C29 ⋊ D5×D15 |
| Sylow | C52 ⋊ C2×D87 |
| Sylow | C3 ⋊ D5×D145 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C29 | C22 |
| LCS | G ▷ C3×C52×C29 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
876 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D1305, #3874⋊D87, C3×D5×D435, … |
| maximal normal subgroup of | C3×D5×D435 |
| maximal quotient of | D5×D1305, C3×D5×D435, D15×D435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 129);