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 ⋊ #10811 |
644 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)(54,57,58,72,60,74,59,73)(55,62,63,71,65,78,64,79)(56,67,68,82,69,84,70,83)(61,75,66,80,77,81,76,85);(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)(54,56,59,70,60,69,58,68)(55,61,63,66,65,77,64,76)(57,67,73,83,74,84,72,82)(62,75,71,80,78,81,79,85);(54,55)(56,66,69,76)(57,71)(58,63)(59,64)(60,65)(61,68,77,70)(62,73)(67,81,84,75)(72,78)(74,79)(80,82,85,83)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=d,d^2=h,e^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eh,g^a=gh,f^b=fh,i^b=i^52,e^c=eh1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75251);