Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#21439678 |
| Fitting, socle, derived | C3×C72×C13 ⋊ C3×C4 |
| Hall | C3×#14274263 ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ C3⋊AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3⋊(#5997⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C13 | C3×C4 |
| prime radical | C3×#16838446 | C2 |
| cosocle | C3×C7⋊D91 | C2×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 546 |
A minimal faithful permutation representation — 2 generators on 30 points:
(2,7,11,8,4,12,5,13,9,3,10,6)(14,15)(16,18,23,25,20,17,21,27,22,19,26,24)(29,30);(1,2,6,9,10,8,13,7,3,4,11,12,5)(14,16,22,26,20,23,21)(15,24,27,19,25,18,17)(28,29,30)Polycyclic presentation:
2,3,2,3,7^2,13|a^2=c,d^a=d^2,e^a=e^5f^3,f^a=e^3f^2,g^a=g^8,e^b=e^4,f^b=f^4,g^b=g^9,e^c=e^6,f^c=f^6,g^c=g^12177 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1091);