Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| isoclinism | isoclinic class of C3⋊#1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×C3⋊#1042 |
| unambiguous semidirect product | C3⋊(C29×#1042) |
| Fitting, socle, Hall | C3×C52×C29 ⋊ C4 |
| derived, Hall | C3×C52 ⋊ C4×C29 |
| Hall | C52×C29 ⋊ Dic3 |
| Hall | C3×C29 ⋊ #1042 |
| Sylow | C52 ⋊ Dic3×C29 |
| Sylow | C3 ⋊ C29×#1042 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C3⋊#1042 |
| commutator, hypocenter | C3×C52 | C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C29 | C4 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C29 | |
52 conjugacy classes of subgroups.
957 conjugacy classes — view the full character table.
| maximal subgroup of | C29×C9⋊#1042, C3×C29×C3⋊#1042, C29×C3⋊(C3⋊#1042) |
| maximal normal subgroup of | C3×C29×C3⋊#1042 |
| maximal quotient of | C29×C9⋊#1042, C3×C29×C3⋊#1042, C29×C3⋊(C3⋊#1042) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 118);