Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13370 |
358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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)(62,64,67,77)(63,68,72,85)(65,79,82,93)(66,83,80,76)(69,86,88,89)(70,84,71,74)(73,87,90,78)(75,91,92,81);(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)(54,56,57,61)(55,58,59,60)(62,63)(64,74)(65,69)(66,71)(67,72)(68,76)(70,80)(73,79)(75,89)(77,84)(78,81)(82,88)(83,85)(86,92)(87,91)(90,93);(54,55,57,59)(56,60,61,58)(62,63)(64,73)(65,78)(66,70)(67,72)(68,75)(69,81)(71,80)(74,79)(76,89)(77,90)(82,87)(83,86)(84,93)(85,92)(88,91)Polycyclic presentation:
2^8,53|a^2=d,b^2=d,c^2=h,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,c^b=cf,f^b=fh,i^b=i^52,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, 88668);