Finite Group DatabasebetaFinite Group Databasebeta| order | 13156 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C23⋊C11)⋊#261 |
| unambiguous semidirect product | (C23⋊#261)⋊C11 |
| Fitting, socle, derived, Hall | C13×C23 ⋊ C4×C11 |
| Hall | C13×C23⋊C11 ⋊ C4 |
| Hall | C23⋊#261 ⋊ C11 |
| Hall | C23⋊C11 ⋊ #261 |
| Sylow | C23 ⋊ C11×#261 |
| Sylow | C13 ⋊ Dic23⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C23 | C4×C11 |
| prime radical | D13×C23⋊C11 | C2 |
| cosocle | C23×D13 | C2×C11 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 299 |
A minimal faithful permutation representation — 2 generators on 36 points:
(2,5,6,13,14,21,16,17,7,18,19,3,4,8,9,20,15,10,22,11,12,23)(25,26,27,29)(28,31,32,33)(30,35,36,34);(1,2,4,7,6,10,12,20,9,15,17,23,19,22,21,13,14,18,16,8,11,5,3)(24,25,28,33,35,26,30,36,29,34,31,32,27)Polycyclic presentation:
2,11,2,13,23|a^2=c,d^a=d^5,e^a=e^22,e^b=e^2,d^c=d^1285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13156, 14);