Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#21439624 |
| Fitting, socle, derived | C3×C72×C13 ⋊ C3×C4 |
| Hall | C3×#14274262 ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ C3⋊AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3⋊#10596873 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C13 | C3×C4 |
| prime radical | C3×#16838474 | C2 |
| cosocle | C3×C72×D13 | C2×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
184 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 546 |
A minimal faithful permutation representation — 2 generators on 30 points:
(2,7,11,8,4,6,5,13,9,3,10,12)(15,16)(18,21,22,19,20,23)(25,26,27)(28,30,29);(1,2,6,9,10,3,7,13,8,4,11,12,5)(14,15,16)(17,18,20,23,22,21,19)(24,25,26,28,27,29,30)Polycyclic presentation:
2,3,2,3,7^2,13|a^2=c,d^a=d^2,e^a=e^6,g^a=g^5,e^b=e^2,f^b=f^2,g^b=g^9,g^c=g^12219 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1227);