Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#21439534 |
| derived | C3×C72×C13 ⋊ C3×C4 |
| Hall | C3×#14274263 ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ Dic3×C13⋊C3 |
| Sylow | C13 ⋊ C3⋊#10596873 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#16838458 |
| commutator, hypocenter | C3×C72×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C13 | C2×C3 |
| prime radical | C2×C3×#14274263 | C2 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 ◁ C2 | |
184 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 1092 |
A minimal faithful permutation representation — 2 generators on 34 points:
(2,3,5)(4,7,10)(6,9,8)(11,13,12)(15,16)(17,18,19,20)(22,25,26,23,24,27)(29,30,31)(32,34,33);(1,2,4,3,6,10,7,11,13,5,8,12,9)(14,15,16)(21,22,24,27,26,25,23)(28,29,30,32,31,33,34)Polycyclic presentation:
2,3^2,7^2,13,2|a^2=g,c^a=c^2,d^a=d^6,d^b=d^2,e^b=e^2,f^b=f^3744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 724);