Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11740 |
358 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 71 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) = 3392 |
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)(54,56,58,57)(55,59,60,61)(62,65,67,79)(63,69,72,86)(64,74,76,77)(66,78,80,93)(68,81,82,83)(70,84,71,85)(73,88,87,91)(75,89,90,92);(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)(56,59)(57,61)(58,60)(62,64,67,76)(63,68,72,82)(65,77,79,74)(66,75,80,90)(69,83,86,81)(70,73,71,87)(78,92,93,89)(84,91,85,88);(55,59,60,61)(62,63,66,71,67,72,80,70)(64,73,75,82,76,87,90,68)(65,69,78,85,79,86,93,84)(74,88,89,83,77,91,92,81)Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=gh,d^2=g,e^2=h,b^a=bd,d^a=df,f^a=fh,c^b=ch,d^b=dg,e^b=efg,i^b=i^52,i^c=i^52,e^d=eh638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79966);