Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C53×#344 ⋊ C2 |
| Sylow | C53 ⋊ #23652 |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,58,60,59)(55,63,65,64)(56,68,70,69)(57,73,74,75)(61,77,78,66)(62,71,79,80)(67,83,72,84)(76,85,82,81);(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)(54,57,58,73,60,74,59,75)(55,62,63,71,65,79,64,80)(56,67,69,84,70,72,68,83)(61,76,66,81,78,82,77,85);(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)(54,56)(55,61)(57,72)(58,68)(59,69)(60,70)(62,76)(63,77)(64,66)(65,78)(67,74)(71,85)(73,84)(75,83)(79,82)(80,81);(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)(54,55,59,64,60,65,58,63)(56,66,68,61,70,77,69,78)(57,71,73,79,74,80,75,62)(67,82,84,85,72,76,83,81)Polycyclic presentation:
2^8,53|a^2=f,c^2=e,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,g^a=gh,i^a=i^52,c^b=cg,e^b=eh,f^b=fh,i^b=i^52,f^c=fh,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 198525);