Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #9088 |
480 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
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)(62,65,68,80)(63,70,72,86)(64,74,76,91)(66,79,67,78)(69,83,85,89)(71,87,81,77)(73,88,84,93)(75,92,82,90);(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)(54,56,57,61,58,55,59,60)(62,64,66,75,68,76,67,82)(63,69,71,73,72,85,81,84)(65,74,79,92,80,91,78,90)(70,83,87,88,86,89,77,93);(54,55,57,60,58,56,59,61)(62,63)(64,73)(65,77,80,87)(66,81)(67,71)(68,72)(69,75)(70,79,86,78)(74,89,91,83)(76,84)(82,85)(88,90,93,92)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=g,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^b=eg,i^b=i^52,d^c=dg,e^c=eg,f^c=fg,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, 64985);