Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #10831 |
628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(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)(55,61,62,68)(56,65)(58,70)(59,69)(60,72,64,76)(63,74,75,81)(66,78)(67,79)(71,82)(73,83,77,84)(80,85);(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)(54,56,58,67,59,66,71,80)(55,60,63,73,62,64,75,77)(57,65,70,79,69,78,82,85)(61,72,74,83,68,76,81,84);(54,55)(56,64,66,60)(57,68)(58,63)(59,62)(61,69)(65,72,78,76)(67,77,80,73)(70,81)(71,75)(74,82)(79,83,85,84)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=d,g^2=h,b^a=bd,c^a=ce,d^a=dh,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, 75346);