Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×#16838417 |
| Fitting | C2×C3×C13×C49 ⋊ C2×C3 |
| derived, Hall | C13×C49 ⋊ C22×C32 |
| Hall | C3×#14274254 ⋊ C22 |
| Hall | C2×C13×D49 ⋊ C32 |
| Hall | C2×D49 ⋊ C3×C13⋊C3 |
| Sylow | C49 ⋊ C22×C3×C13⋊C3 |
| Sylow | C13 ⋊ C2×C3×D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #16838417 |
| commutator, cosocle, hypocenter | C13×C49 | C22×C32 |
| Frattini | C7 | C2×C3×#10587720 |
| Fitting | C2×C3×C13×C49 | C2×C3 |
| socle | C2×C3×C7×C13 | AGL(1,𝔽7) |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C2×C3 | |
180 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3822 |
708 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 189);