Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #8519 |
754 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 107 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) = 3392 |
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)(54,57,58,65)(55,60,61,67)(56,63,64,69)(59,66,62,68)(70,72)(71,76)(73,80)(74,81)(75,77)(78,79)(82,83)(84,85);(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)(54,56,58,64)(55,59,61,62)(57,63,65,69)(60,66,67,68)(70,72)(71,75)(73,82)(74,81)(76,77)(78,84)(79,85)(80,83);(54,55)(56,62,64,59)(57,60)(58,61)(63,68,69,66)(65,67)(70,71)(72,79,81,76)(73,77)(74,78)(75,80,84,82)(83,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=g,d^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,f^b=fgh,i^b=i^52,f^c=fh,i^c=i^52710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62074);