Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C3×C11×C49⋊C3 |
| Fitting | C22×C3×C11×C49 ⋊ C3 |
| derived, Sylow | C49 ⋊ C22×C32×C11 |
| Hall | C22×C11×C49 ⋊ C32 |
| Hall | C11×C49 ⋊ C22×C32 |
| Hall | C22×C49 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C11 | C49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C22×C32×C11 |
| Frattini | C7 | C22×C3×C11×ΓL(1,𝔽8) |
| Fitting | C22×C3×C11×C49 | C3 |
| socle | C22×C3×C7×C11 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C22×C3×C11 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6468 |
2508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 100);