Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1333 ⋊ C2 |
| Sylow | C53 ⋊ #12350 |
298 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 93 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)(55,57)(58,61)(59,60)(65,78)(69,88)(72,91)(73,83)(76,90)(77,93)(80,86)(87,92);(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)(54,55,59,61)(56,57,60,58)(62,64,67,74)(63,68,71,84)(65,77,78,93)(66,82,79,75)(69,87,88,92)(70,89,81,85)(72,90,91,76)(73,86,83,80);(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)(55,56)(57,58)(60,61)(62,63,67,71)(64,72,74,91)(65,76,78,90)(66,81,79,70)(68,83,84,73)(69,86,88,80)(75,92,82,87)(77,89,93,85)Polycyclic presentation:
2^8,53|a^2=h,b^2=g,d^2=fh,e^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=egh,f^a=fh,i^a=i^52,d^b=df,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=egh,i^c=i^52863 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83233);