Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#2245 ⋊ C2 |
| Sylow | C53 ⋊ #33705 |
578 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 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)(64,76)(65,79)(70,85)(71,88)(77,92)(78,80)(86,93)(87,89);(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)(55,59)(58,61)(62,65,66,80,81,92,83,76,69,79,82,78,68,77,67,64)(63,71,72,89,84,93,91,85,75,88,90,87,74,86,73,70);(54,56,57,60)(55,58,59,61)(62,64,67,77,68,78,82,79,69,76,83,92,81,80,66,65)(63,70,73,86,74,87,90,88,75,85,91,93,84,89,72,71);(54,55)(56,58)(57,59)(60,61)(62,63,69,75)(64,71,76,88)(65,70,79,85)(66,73,82,91)(67,72,83,90)(68,84,81,74)(77,89,92,87)(78,93,80,86)Polycyclic presentation:
2^8,53|a^2=h,b^2=f,c^2=e,e^2=gh,f^2=g,g^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fgh,g^a=gh,d^b=dh,d^c=dh,i^c=i^52,i^d=i^52728 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324925);