Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D15×D145 |
| 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 ⋊ D3×D29 |
| 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.
666 conjugacy classes — view the full character table.
| maximal subgroup of | D45×D145, #39908060, C3×D15×D145, … |
| maximal normal subgroup of | C3×D15×D145 |
| maximal quotient of | D45×D145, C3×D15×D145, D15×D435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 130);