Finite Group DatabasebetaFinite Group Databasebeta| order | 13156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D143⋊D23 |
| unambiguous semidirect product | D253⋊D13 |
| unambiguous semidirect product | D299⋊D11 |
| Fitting, socle, derived, Hall | C11×C13×C23 ⋊ C22 |
| Hall | C13×C23 ⋊ C2×D11 |
| Hall | C11×C23 ⋊ C2×D13 |
| Hall | C11×C13 ⋊ C2×D23 |
| Sylow | C23 ⋊ D11×D13 |
| Sylow | C13 ⋊ D11×D23 |
| Sylow | C11 ⋊ D13×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13×C23 | C22 |
| LCS | G ▷ C11×C13×C23 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 3289 |
A minimal faithful permutation representation — 2 generators on 47 points:
(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(38,39)(40,41)(42,43)(44,45)(46,47);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38,40,42,44,46,47,45,43,41,39)Polycyclic presentation:
2^2,11,13,23|d^a=d^12,e^a=e^22,c^b=c^10,d^b=d^12859 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13156, 31);