Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2070 ⋊ C2 |
| Sylow | C53 ⋊ #30236 |
446 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 125 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)(54,57,58,70,59,71,72,83)(55,62,63,77,61,75,64,76)(56,67,66,80,69,81,68,82)(60,73,65,79,74,84,78,85);(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)(55,61)(56,66)(57,70)(58,72)(60,65)(62,76)(67,81)(68,69)(71,83)(73,84)(74,78)(75,77);(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)(55,60,61,74)(57,67)(58,66)(59,69)(62,73,75,84)(63,65,64,78)(68,72)(70,80)(71,81)(76,85,77,79)(82,83);(54,55,58,63,59,61,72,64)(56,65,68,60,69,78,66,74)(57,62,70,77,71,75,83,76)(67,79,82,73,81,85,80,84)Polycyclic presentation:
2^8,53|a^2=fg,b^2=f,d^2=e,e^2=h,g^2=h,b^a=be,c^a=cf,f^a=fh,g^a=gh,c^b=cg,g^b=gh,i^b=i^52,d^c=de,e^c=eh,g^c=gh,i^c=i^52,i^d=i^52632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 281710);