Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2026 ⋊ C2 |
| Sylow | C53 ⋊ #29643 |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 89 points:
(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)(61,69)(64,71)(67,73)(70,72)(76,83)(80,88)(82,89)(84,87);(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)(55,57)(58,61)(59,64)(60,67)(62,69)(63,70)(65,71)(66,72)(68,73)(74,76,77,83)(75,80,79,88)(78,87,85,84)(81,89,86,82);(54,55)(56,57)(58,60,62,68)(59,63,65,66)(61,67,69,73)(64,70,71,72)(75,79)(80,88)(81,86)(82,89);(58,59,62,65)(60,66,68,63)(61,64,69,71)(67,72,73,70)(74,75,77,79)(76,82,83,89)(78,86,85,81)(80,87,88,84)Polycyclic presentation:
2^8,53|a^2=e,b^2=eh,c^2=h,f^2=h,b^a=be,c^a=cf,f^a=fh,c^b=cg,d^c=de,f^c=fh,i^d=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 275335);