Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C3×#15668530 |
| Fitting, socle, Hall | C3×C52×C29 ⋊ C4 |
| derived, Hall | C52×C29 ⋊ C3×C4 |
| Hall | C3×C29 ⋊ #1044 |
| Hall | C3×C52 ⋊ Dic29 |
| Sylow | C29 ⋊ C3×#1044 |
| Sylow | C52 ⋊ C3×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15668530 |
| commutator, hypocenter | C52×C29 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C29 | C4 |
| LCS | G ▷ C52×C29 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
618 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#15668530, C3×#22576425, C32×#15668530, … |
| maximal normal subgroup of | C9×#15668530, C32×#15668530 |
| maximal quotient of | C9×#15668530, C32×#15668530, C3×C3⋊#15668530 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 89);