Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D7×D63 |
| unambiguous semidirect product | (C7×D7)⋊(C11×D9) |
| unambiguous semidirect product | (C9×D7)⋊(C11×D7) |
| Fitting, Hall | C72×C9×C11 ⋊ C22 |
| derived, Hall | C72×C9 ⋊ C22×C11 |
| Hall | C72×C11 ⋊ C2×D9 |
| Hall | C9×C11 ⋊ D72 |
| Sylow | C72 ⋊ C2×C11×D9 |
| Sylow | C9 ⋊ C11×D72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D7×D63 |
| commutator, cosocle, hypocenter | C72×C9 | C22×C11 |
| Frattini | C3 | C11×D7×D21 |
| Fitting | C72×C9×C11 | C22 |
| socle | C3×C72×C11 | C2×D3 |
| LCS | G ▷ C72×C9 | |
| UCS | C1 ◁ C11 | |
156 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1386 |
1815 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 209);