Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3407 ⋊ C2 |
| Sylow | C53 ⋊ #13068 |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 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)(54,57)(55,61)(56,66)(58,75)(59,74)(60,73)(62,80)(63,70)(64,79)(65,81)(67,84)(68,83)(69,78)(71,77)(72,76)(82,85);(54,56,65,55,59,68,77,63,60,69,82,64,76,67,58,62)(57,66,81,61,74,83,71,70,73,78,85,79,72,84,75,80);(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)(56,65)(57,70,73,80)(58,68)(59,62)(60,64)(61,72,79,74)(63,76)(66,75,78,71)(67,77)(69,82)(81,83,85,84)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=gh,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,e^b=eh,d^c=dh,e^c=eh,f^c=fh1814 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86975);