Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D7×C3⋊D231 |
| unambiguous semidirect product | (C3×D7)⋊D231 |
| unambiguous semidirect product | (C7×D7)⋊(C3⋊D33) |
| unambiguous semidirect product | (C11×D7)⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C72×C11 ⋊ C22 |
| Hall | C72×C11 ⋊ C2×C3⋊D3 |
| Hall | C32×C72 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ D72 |
| Sylow | C72 ⋊ C2×C3⋊D33 |
| Sylow | C11 ⋊ D7×C3⋊D21 |
| Sylow | C32 ⋊ D7×D77 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C72×C11 | C22 |
| LCS | G ▷ C32×C72×C11 | |
| UCS | C1 | |
312 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1386 |
1740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 517);