Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #21483 |
1328 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,58,59,72,60,55,63,64)(56,66,68,81,67,61,74,75)(57,69,71,82,70,62,76,77)(65,78,80,85,79,73,83,84);(54,57)(55,62)(56,65)(58,69)(59,71)(60,70)(61,73)(63,76)(64,77)(66,78)(67,79)(68,80)(72,82)(74,83)(75,84)(81,85);(54,56)(55,61)(57,65)(58,66)(59,68)(60,67)(62,73)(63,74)(64,75)(69,78)(70,79)(71,80)(72,81)(76,83)(77,84)(82,85);(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)(54,55,59,64,60,58,63,72)(56,61,68,75,67,66,74,81)(57,62,71,77,70,69,76,82)(65,78,80,85,79,73,83,84)Polycyclic presentation:
2^8,53|a^2=g,d^2=g,g^2=h,b^a=be,c^a=cf,i^a=i^52,f^b=fh,e^c=eh,i^d=i^52896 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 175579);