Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2888 ⋊ C2 |
| Sylow | C53 ⋊ #21779 |
1270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(55,62)(58,71)(60,64)(61,75)(67,70)(68,82)(72,74)(80,81);(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)(54,57,59,69)(55,61,62,75)(56,65,66,79)(58,68,71,82)(60,72,64,74)(63,76,77,85)(67,80,70,81)(73,83,78,84);(54,56)(55,60)(57,65)(58,70)(59,66)(61,74)(62,64)(63,78)(67,71)(68,81)(69,79)(72,75)(73,77)(76,83)(80,82)(84,85);(54,55,58,63,59,62,71,77)(56,64,67,78,66,60,70,73)(57,61,68,76,69,75,82,85)(65,72,80,83,79,74,81,84)Polycyclic presentation:
2^8,53|a^2=g,c^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=ce,f^b=fh,g^b=gh,i^c=i^52,g^d=gh1112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 178734);