Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #8677 |
366 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(54,55,57,59)(56,61,60,58)(62,65,67,79)(63,69,71,77)(64,74,76,90)(66,78,73,87)(68,81,82,91)(70,83,80,92)(72,84,85,88)(75,89,86,93);(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)(62,64,73,86,67,76,66,75)(63,68,80,85,71,82,70,72)(65,74,87,93,79,90,78,89)(69,81,92,88,77,91,83,84);(55,58)(56,60)(59,61)(62,63)(64,72)(65,77,79,69)(66,80)(67,71)(68,75)(70,73)(74,88,90,84)(76,85)(78,83,87,92)(81,89,91,93)(82,86)Polycyclic presentation:
2^8,53|a^2=f,b^2=dg,c^2=h,d^2=g,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^b=i^52,e^c=egh,f^c=fg878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62785);