Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #10905 |
672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2)(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)(54,57,59,71,60,72,58,74)(55,62,63,78,64,79,73,70)(56,66,68,82,69,84,67,83)(61,75,65,80,77,81,76,85);(54,56)(55,61,64,77)(57,66)(58,67)(59,68)(60,69)(62,75,79,81)(63,65,73,76)(70,85,78,80)(71,82)(72,84)(74,83);(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)(54,55,59,63,60,64,58,73)(56,65,68,77,69,76,67,61)(57,70,71,62,72,78,74,79)(66,81,82,85,84,75,83,80)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=f,d^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,i^a=i^52,e^b=eh,d^c=dh,e^c=eh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75713);