Finite Group DatabasebetaFinite Group Databasebeta| order | 17802 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D23×C43⋊C3 |
| unambiguous semidirect product | C23⋊(C2×C3×C43⋊C3) |
| unambiguous semidirect product | (C43×D23)⋊C32 |
| unambiguous semidirect product | (C3×C43×D23)⋊C3 |
| Fitting, socle | C3×C23×C43 ⋊ C2×C3 |
| derived, Hall | C23×C43 ⋊ C2×C32 |
| Hall | C3×C23×C43⋊C3 ⋊ C2 |
| Hall | C43×D23 ⋊ C32 |
| Sylow | C43 ⋊ C32×D23 |
| Sylow | C23 ⋊ C2×C3×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D23×C43⋊C3 |
| commutator, cosocle, hypocenter | C23×C43 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C43 | C2×C3 |
| LCS | G ▷ C23×C43 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2967 |
663 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D23×D43⋊C3, D23×C3⋊(D43⋊C3), D3×D23×C43⋊C3, … |
| maximal normal subgroup of | C3×D23×D43⋊C3, D23×C3⋊(D43⋊C3), D3×D23×C43⋊C3, … |
| maximal quotient of | C3×Dic23×C43⋊C3, C2×C3×D23×C43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17802, 16);