Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic145 |
| derived | C5×C29 ⋊ C3×C4×C5 |
| Hall | C3×C52×C29 ⋊ C4 |
| Hall | C52×C29 ⋊ C3×C4 |
| Hall | C3×C29 ⋊ C5×Dic5 |
| Hall | C3×C52 ⋊ Dic29 |
| Sylow | C29 ⋊ C3×C5×Dic5 |
| Sylow | C52 ⋊ C3×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D145 |
| commutator, hypocenter | C5×C29 | C3×C4×C5 |
| Frattini | C2 | C3×C5×D145 |
| Fitting, socle | C2×C3×C52×C29 | C2 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C2×C3×C5 | |
64 conjugacy classes of subgroups.
2220 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C9×Dic145, C3×#22576397, C3×C5×Dic435, … |
| maximal normal subgroup of | C5×C9×Dic145, C32×C5×Dic145 |
| maximal quotient of | C5×C9×Dic145, C3×C5×Dic435, C32×C5×Dic145 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 46);