Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2952 ⋊ C2 |
| Sylow | C53 ⋊ #33469 |
646 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)(56,65)(61,78)(64,82)(66,69)(74,79)(77,85)(80,81)(83,84);(54,56,58,64,59,65,71,82)(55,61,72,81,62,78,63,80)(57,69,67,84,70,66,73,83)(60,74,68,85,75,79,76,77);(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)(54,55)(56,61)(57,68)(58,72)(59,62)(60,73)(63,71)(64,81)(65,78)(66,77)(67,75)(69,85)(70,76)(74,83)(79,84)(80,82);(55,60,62,75)(56,64)(57,67)(58,71)(61,77,78,85)(63,68,72,76)(65,82)(66,69)(70,73)(74,81,79,80)Polycyclic presentation:
2^8,53|a^2=f,c^2=fg,e^2=g,g^2=h,b^a=be,c^a=cg,e^a=eg,g^a=gh,e^b=egh,f^b=fh,g^b=gh,i^b=i^52,d^c=dh,e^c=eh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323025);