Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #10747 |
1214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,61)(59,65)(60,69)(62,73)(63,72)(64,76)(66,79)(67,78)(68,82)(70,83)(71,84)(74,86)(75,85)(77,87)(80,89)(81,88);(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)(54,55,56,57)(58,60)(59,64)(61,69)(62,74)(63,70)(65,76)(66,68)(67,81)(71,75)(72,83)(73,86)(77,80)(78,88)(79,82)(84,85)(87,89);(58,59,62,67,63,66,75,80)(60,68,71,81,70,64,74,77)(61,65,73,78,72,79,85,89)(69,76,84,87,83,82,86,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh1520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74920);