Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2115 ⋊ C2 |
| Sylow | C53 ⋊ #13391 |
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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)(54,57,58,56,61,68,60,70)(55,63,64,82,66,83,73,79)(59,69,74,84,77,85,76,72)(62,78,67,81,71,65,80,75);(54,56)(55,62)(57,58)(59,69)(60,68)(61,70)(63,81)(64,80)(65,79)(66,71)(67,73)(72,74)(75,83)(76,84)(77,85)(78,82);(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)(54,55)(56,67)(57,71)(58,73)(59,75)(60,64)(61,66)(62,68)(63,72)(65,74)(69,79)(70,80)(76,78)(77,81)(82,85)(83,84)Polycyclic presentation:
2^8,53|c^2=d,d^2=h,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,i^a=i^52,c^b=cf,d^b=dh,f^b=fh,e^c=egh,g^c=gh,i^c=i^521178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88801);