Finite Group DatabasebetaFinite Group Databasebeta| order | 13340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#10596814 |
| Fitting, socle, derived, Hall | C5×C23×C29 ⋊ C4 |
| Hall | C23×C29 ⋊ AGL(1,𝔽5) |
| Hall | C5×C29 ⋊ Dic23 |
| Hall | C5×C23 ⋊ #1181 |
| Sylow | C29 ⋊ C23⋊AGL(1,𝔽5) |
| Sylow | C23 ⋊ #10596814 |
| Sylow | C5 ⋊ C23⋊#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C23×C29 | C4 |
| prime radical, cosocle | C23×D145 | C2 |
| LCS | G ▷ C5×C23×C29 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 3335 |
A minimal faithful permutation representation — 2 generators on 57 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,26)(14,19,21,23)(16,24,25,20)(22,27,28,29)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(54,55,56,57);(1,2,5,10,19,8,16,26,29,28,21,13,6,11,20,24,12,3,7,14,22,27,17,25,15,23,18,9,4)(30,31,33,35,37,39,41,43,45,47,49,51,52,50,48,46,44,42,40,38,36,34,32)(53,54,55,57,56)Polycyclic presentation:
2^2,5,23,29|a^2=b,c^a=c^2,d^a=d^22,e^a=e^17,c^b=c^4,e^b=e^28854 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13340, 18);