Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C7×C11 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C3×C7×C11×ΓL(1,𝔽8) |
| Fitting, socle | C22×C3×C72×C11 ⋊ C3 |
| derived | C7 ⋊ C22×C32×C7×C11 |
| Hall | C22×C72×C11 ⋊ C32 |
| Hall | C72×C11 ⋊ C22×C32 |
| Hall | C22×C72 ⋊ C32×C11 |
| Sylow | C72 ⋊ C22×C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C7×C11 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C22×C32×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C72×C11 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C22×C3×C7×C11 | |
280 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2772 |
4620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 562);