Finite Group DatabasebetaFinite Group Databasebeta| order | 9204 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13×C59 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C13×C59 |
| unambiguous semidirect product | C3⋊(C4×C13×C59) |
| derived, Sylow | C3 ⋊ C4×C13×C59 |
| Hall | C3×C13×C59 ⋊ C4 |
| Hall | C3×C59 ⋊ C4×C13 |
| Hall | C3×C13 ⋊ C4×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13×C59 | D3 |
| commutator, hypocenter | C3 | C4×C13×C59 |
| Frattini | C2 | D3×C13×C59 |
| Fitting, socle | C2×C3×C13×C59 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C13×C59 | |
24 conjugacy classes of subgroups.
4602 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×Dic9×C59, Dic3×C13⋊C3×C59, C13×C3⋊Dic3×C59, … |
| maximal normal subgroup of | Dic3×C13⋊C3×C59, C3×Dic3×C13×C59 |
| maximal quotient of | C13×Dic9×C59, C13×C3⋊Dic3×C59, C3×Dic3×C13×C59 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9204, 6);