Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#430 ⋊ C2 |
| Sylow | C53 ⋊ #20860 |
1296 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)(55,63)(61,75)(62,77)(64,71)(65,76)(74,85)(78,79)(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)(55,62)(56,66)(58,73)(59,69)(60,70)(61,74)(63,77)(64,79)(65,80)(67,84)(68,83)(71,78)(72,82)(75,85)(76,81);(54,56,59,67,60,68,58,72)(55,61,64,76,63,75,71,65)(57,66,69,84,70,83,73,82)(62,74,79,81,77,85,78,80);(54,55,59,64,60,63,58,71)(56,65,67,61,68,76,72,75)(57,62,69,79,70,77,73,78)(66,81,84,85,83,80,82,74)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,e^b=eh,f^b=fh,e^c=eh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 170413);