Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #10777 |
1178 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)(58,61,64,77)(59,66,67,81)(60,71,73,87)(62,76,63,75)(65,79,70,84)(68,82,69,74)(72,88,78,86)(80,85,83,89);(54,55,56,57)(58,60)(59,65)(61,71)(62,72)(63,78)(64,73)(66,79)(67,70)(68,80)(69,83)(74,89)(75,86)(76,88)(77,87)(81,84)(82,85);(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)(58,59,63,69,64,67,62,68)(60,70,72,83,73,65,78,80)(61,74,76,66,77,82,75,81)(71,85,86,79,87,89,88,84)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^52,f^b=fh,e^c=eh,f^c=fh1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75059);