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 ⋊ #12887 |
286 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)(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)(55,59)(58,61)(62,65,66,81,67,64,76,77,68,79,75,91,84,78,92,90)(63,70,71,80,72,87,82,89,73,88,85,93,83,69,86,74);(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)(54,56,57,60)(55,58,59,61)(62,64,75,90,67,79,92,81,68,78,66,77,84,65,76,91)(63,69,85,89,72,70,86,93,73,87,71,74,83,88,82,80);(54,55)(56,58)(57,59)(60,61)(62,63)(64,74,78,89)(65,80,79,93)(66,82)(67,83)(68,73)(69,77,87,90)(70,81,88,91)(71,76)(72,84)(75,86)(85,92)Polycyclic presentation:
2^8,53|a^2=f,b^2=eh,c^2=d,d^2=g,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,f^b=fh,i^b=i^52,f^c=fh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85943);