Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2209 ⋊ C2 |
| Sylow | C53 ⋊ #33583 |
702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 89 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)(58,61,64,63)(59,66,69,68)(60,71,73,79)(62,74,78,77)(65,81,82,86)(67,83,85,75)(70,84,87,88)(72,76,80,89);(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)(58,60)(59,65)(61,71)(62,76)(63,79)(64,73)(66,81)(67,84)(68,86)(69,82)(70,75)(72,77)(74,80)(78,89)(83,87)(85,88);(54,55,56,57);(55,57)(58,59,64,69)(60,70,73,87)(61,68,63,66)(62,75,78,83)(65,80,82,72)(67,74,85,77)(71,88,79,84)(76,86,89,81)Polycyclic presentation:
2^8,53|a^2=h,b^2=e,d^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,d^a=dh,f^a=fg,g^a=gh,f^c=fg,g^c=gh,i^c=i^52,i^d=i^52800 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323864);