Finite Group DatabasebetaFinite Group Databasebeta| order | 9204 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×Dic59 |
| unambiguous semidirect product | C59⋊(C3×C4×C13) |
| derived, Sylow | C59 ⋊ C3×C4×C13 |
| Hall | C3×C13×C59 ⋊ C4 |
| Hall | C13×C59 ⋊ C3×C4 |
| Hall | C3×C59 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C13 | D59 |
| commutator, hypocenter | C59 | C3×C4×C13 |
| Frattini | C2 | C3×C13×D59 |
| Fitting, socle | C2×C3×C13×C59 | C2 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C3×C13 | |
24 conjugacy classes of subgroups.
2418 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C13×Dic59, C13⋊C9×Dic59, C3×C13⋊C3×Dic59, … |
| maximal normal subgroup of | C9×C13×Dic59, C13⋊C9×Dic59, C3×C13⋊C3×Dic59, … |
| maximal quotient of | C9×C13×Dic59, C3×C13×Dic177, C32×C13×Dic59 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9204, 3);