Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#1398 ⋊ C2 |
| Sylow | C53 ⋊ #7390 |
128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 43 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 — 2 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)(55,62)(56,69)(57,58)(59,60)(63,77)(64,83)(65,82)(66,68)(67,81)(70,76)(71,73)(72,85)(74,75)(78,80)(79,84);(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)(54,55,57,64,59,66,70,84,61,67,76,65,60,78,58,77)(56,68,69,82,72,62,71,79,74,80,75,83,73,81,85,63)Polycyclic presentation:
2^8,53|a^2=d,c^2=eh,d^2=f,e^2=g,f^2=h,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^a=i^52,c^b=ceg,d^b=dg,e^b=egh,f^b=fh,g^b=gh,i^b=i^52,d^c=dh1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57040);