Finite Group DatabasebetaFinite Group Databasebeta| order | 13524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊((C49⋊C3)⋊C4) |
| unambiguous semidirect product | (C49⋊C3)⋊Dic23 |
| unambiguous semidirect product | Dic1127⋊C3 |
| derived, Hall | C23×C49 ⋊ C3×C4 |
| Hall | Dic1127 ⋊ C3 |
| Hall | C23×C49⋊C3 ⋊ C4 |
| Hall | C49⋊C3 ⋊ Dic23 |
| Sylow | C49 ⋊ C3×Dic23 |
| Sylow | C23 ⋊ (C49⋊C3)⋊C4 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 76 |
| transitive degree | μt(G) = 4508 |
A minimal faithful permutation representation — 2 generators on 76 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(25,33,35,27,28,36)(26,45,47,31,32,48)(29,57,44,38,39,66)(30,62,63,42,43,72)(34,41,40,46,51,59)(37,60,69,55,56,70)(49,61,64,67,50,53)(52,65,54,68,58,71)(73,74,75,76);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,46,43,54,53,58,27,31,68,37,36,63,38,42,45,69,28,57,59,51,66,47,67,61,60,56,50,49,48,44,41,40,39,33,70,32,30,29,72,35,55,52,26,25,65,64,71,62,34)Polycyclic presentation:
2,3,7,23,2,7|a^2=e,c^7=f^6,c^a=c^6f,d^a=d^22,f^a=f^6,c^b=c^2f^3,f^b=f^2446 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13524, 4);