Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1340 ⋊ C2 |
| Sylow | C53 ⋊ #11685 |
448 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(54,57,60,59)(55,62,64,75)(56,66,68,69)(58,70,73,74)(61,76,78,77)(63,71,80,85)(65,81,82,79)(67,72,84,83);(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)(54,56)(55,61)(57,66)(58,72)(59,69)(60,68)(62,76)(63,79)(64,78)(65,71)(67,74)(70,84)(73,83)(75,77)(80,81)(82,85);(54,55)(56,65,68,82)(57,62)(58,71,73,85)(59,75)(60,64)(61,67)(63,70,80,74)(66,81,69,79)(72,76)(77,83)(78,84)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,d^2=gh,f^2=h,g^2=h,b^a=bd,d^a=df,g^a=gh,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^b=i^52,i^c=i^52,e^d=eh560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79717);