Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12876 |
370 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 119 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)(54,56,59,68,60,66,58,69)(55,61,63,80,64,76,75,77)(57,72,74,67,71,83,73,82)(62,79,70,65,78,84,85,81);(57,71)(62,78)(65,81)(67,82)(70,85)(72,83)(73,74)(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)(54,55,58,63,60,64,59,75)(56,65,68,79,66,81,69,84)(57,70,73,78,71,85,74,62)(61,72,77,67,76,83,80,82)Polycyclic presentation:
2^8,53|a^2=f,c^2=dg,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^a=i^52,e^b=eh,d^c=dh,e^c=eg,f^c=fh,g^c=gh,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85901);