Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1996 ⋊ C2 |
| Sylow | C53 ⋊ #9934 |
808 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 77 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)(55,58)(57,60)(59,61)(63,69)(65,66)(68,72)(70,71)(73,75)(76,77);(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)(58,61)(62,64)(63,68)(65,75)(66,73)(67,74)(69,77)(70,72)(71,76);(54,55)(56,58)(57,59)(60,61)(62,63,67,71)(64,72,74,77)(65,70,66,69)(68,75,76,73)Polycyclic presentation:
2^8,53|a^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fh,c^b=cf,d^b=dg,i^b=i^52,d^c=dh,e^c=eg,i^c=i^52863 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 69903);