Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#21439672 |
| Fitting, socle | C3×C72×C13 ⋊ Dic3 |
| derived | C13×#3862 ⋊ C3×C4 |
| Hall | C3×C13×#3862 ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Hall | C3×#3862 ⋊ #261 |
| Sylow | C72 ⋊ C3×C3⋊#261 |
| Sylow | C13 ⋊ C3×#10596868 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #21439672 |
| commutator, hypocenter | C13×#3862 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | Dic3 |
| prime radical | C3×D13×#3862 | C2 |
| cosocle | D13×#3862 | C2×C3 |
| LCS | G ▷ C13×#3862 | |
| UCS | C1 ◁ C3 | |
104 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 546 |
291 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 969);