Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D539 |
| Fitting, derived, Hall | C32×C11×C49 ⋊ C22 |
| Hall | C11×C49 ⋊ C2×C3⋊D3 |
| Hall | C32×C49 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D49 |
| Sylow | C49 ⋊ C3⋊D3×D11 |
| Sylow | C11 ⋊ C3⋊D3×D49 |
| Sylow | C32 ⋊ C2×D539 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C11×C49 | C22 |
| Frattini | C7 | C3⋊D3×D77 |
| socle | C32×C7×C11 | C2×D7 |
| LCS | G ▷ C32×C11×C49 | |
| UCS | C1 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4851 |
1626 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 82);