Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1391 ⋊ C2 |
| Sylow | C53 ⋊ #13351 |
710 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 77 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:
(2,8)(5,18)(7,20)(9,23)(10,11)(12,26)(13,19)(14,30)(16,31)(21,22)(24,25)(27,28)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84);(1,3)(2,7)(4,13)(5,14)(6,15)(8,22)(9,12)(10,20)(11,21)(16,29)(17,19)(18,30)(23,26)(24,27)(25,28)(31,32)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85);(1,2,6,11)(3,12,15,28)(4,9,17,25)(5,8,18,10)(7,19,21,13)(14,26,30,27)(16,23,31,24)(20,29,22,32)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)Polycyclic presentation:
2^8,53|a^2=h,e^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,i^a=i^52,c^b=cf,g^b=gh,i^b=i^52,d^c=dg,e^c=eh,i^c=i^52,f^d=fh704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88561);