Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #10471 |
366 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 91 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)(55,59)(57,61)(58,60)(62,65,66,80,68,81,67,82)(63,70,71,87,72,78,83,92)(64,74,75,90,77,91,76,79)(69,84,73,86,85,93,88,89);(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)(55,58)(59,60)(62,64,68,77)(63,69,72,85)(65,79,81,90)(66,76,67,75)(70,86,78,89)(71,88,83,73)(74,80,91,82)(84,92,93,87);(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)(54,55,56,58)(57,59,61,60)(62,63)(64,73)(65,78)(66,83)(67,71)(68,72)(69,75)(70,81)(74,89)(76,85)(77,88)(79,84)(80,87)(82,92)(86,91)(90,93)Polycyclic presentation:
2^8,53|a^2=h,b^2=g,c^2=dh,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^52,c^b=cf,d^b=dg,f^b=fg,i^b=i^52,e^c=egh,i^c=i^52869 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 73354);