Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C72×D9×D11 |
| unambiguous semidirect product | (C11×D9)⋊(C2×C72) |
| unambiguous semidirect product | (C9×D11)⋊(C2×C72) |
| unambiguous semidirect product | D99⋊(C2×C72) |
| Fitting, Hall | C72×C9×C11 ⋊ C22 |
| derived, Hall | C9×C11 ⋊ C22×C72 |
| Hall | C72×C11 ⋊ C2×D9 |
| Hall | C72×C9 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C72×D9 |
| Sylow | C9 ⋊ C2×C72×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D9×D11 |
| commutator, cosocle, hypocenter | C9×C11 | C22×C72 |
| Frattini | C3 | D3×C72×D11 |
| Fitting | C72×C9×C11 | C22 |
| socle | C3×C72×C11 | C2×D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C72 | |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4851 |
2058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 198);