Finite Group DatabasebetaFinite Group Databasebeta| order | 9204 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×Dic59 |
| unambiguous semidirect product | C59⋊(C4×C13⋊C3) |
| unambiguous semidirect product | (C13×Dic59)⋊C3 |
| derived, Hall | C13×C59 ⋊ C3×C4 |
| Hall | C13×Dic59 ⋊ C3 |
| Hall | C13⋊C3×C59 ⋊ C4 |
| Sylow | C59 ⋊ C4×C13⋊C3 |
| Sylow | C13 ⋊ C3×Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C13⋊C3×D59 |
| commutator, hypocenter | C13×C59 | C3×C4 |
| Fitting, socle | C2×C13×C59 | C2×C3 |
| LCS | G ▷ C13×C59 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
434 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C13⋊C3×Dic59, C13⋊C3×Dic177 |
| maximal normal subgroup of | C3×C13⋊C3×Dic59 |
| maximal quotient of | C13⋊C9×Dic59, C3×C13⋊C3×Dic59, C13⋊C3×Dic177 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9204, 10);