Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12668 |
308 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)(54,57,72,58,61,73,60,59)(55,63,79,64,66,80,67,65)(56,69,70,74,71,85,76,75)(62,68,78,81,77,84,83,82);(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)(55,62,66,77)(57,69)(58,74)(59,75)(60,76)(61,71)(63,68,80,84)(64,81,65,82)(67,83,79,78)(70,72)(73,85);(54,55,59,65,60,67,73,80,61,66,58,64,72,79,57,63)(56,68,69,78,70,81,74,77,71,84,85,83,76,82,75,62)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,g^2=h,b^a=bd,f^a=fh,d^b=dg,e^b=egh,g^b=gh,i^b=i^522144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84947);