Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #12579 |
736 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)(56,65)(60,64)(66,71)(67,79)(72,76)(73,78)(80,82)(84,85);(54,56,58,67,59,65,70,79)(55,60,63,73,61,64,75,78)(57,66,69,80,68,71,81,82)(62,76,77,85,74,72,83,84);(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)(54,55,57,62,59,61,68,74)(56,64,66,76,65,60,71,72)(58,63,69,77,70,75,81,83)(67,78,80,85,79,73,82,84)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,e^2=h,f^2=h,b^a=bd,d^a=dg,g^a=gh,i^a=i^52,c^b=ch,e^b=eg,e^d=eh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84532);