Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×AGL(1,𝔽7)×D21 |
| unambiguous semidirect product | D7⋊(C3×C11×D21) |
| unambiguous semidirect product | (C3×AGL(1,𝔽7))⋊(C11×D7) |
| unambiguous semidirect product | (C7×AGL(1,𝔽7))⋊(D3×C11) |
| Fitting, socle | C3×C72×C11 ⋊ C22×C3 |
| derived | C3×C72 ⋊ C22×C3×C11 |
| Hall | C3×C7×C11×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C72×C11 ⋊ C2×C3×D3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C22×C11 |
| Sylow | C72 ⋊ C2×C3×D3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | AGL(1,𝔽7)×D21 |
| commutator, cosocle, hypocenter | C3×C72 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C11 | C22×C3 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C11 | |
184 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1386 |
924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 390);