Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #33941 |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56,57,61)(55,59,58,60);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(62,64,67,73)(63,68,71,84)(65,77,80,93)(66,82,78,75)(69,87,88,92)(70,89,81,85)(72,91,90,76)(74,86,83,79);(54,55,57,58)(56,60,61,59)(64,73)(68,84)(72,90)(74,83)(75,82)(77,93)(85,89)(87,92);(55,58)(59,60)(62,63,67,71)(64,72,73,90)(65,76,80,91)(66,81,78,70)(68,83,84,74)(69,86,88,79)(75,92,82,87)(77,89,93,85)Polycyclic presentation:
2^8,53|a^2=h,b^2=e,c^2=h,d^2=e,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,c^b=ch,d^b=de,f^c=fg,g^c=gh,i^c=i^52953 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 327377);