Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #12660 |
330 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)(54,56,57,55)(59,65)(60,69,70,72)(61,74)(64,77,68,81)(67,79)(71,86,85,84)(75,83)(78,89,82,88);(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)(58,60,61,71,62,72,75,86,63,70,74,85,76,69,83,84)(59,64,66,78,67,77,80,88,65,68,73,82,79,81,87,89);(54,55,57,56)(58,59)(60,68)(61,73)(62,67)(63,65)(64,70)(66,74)(69,77)(71,78)(72,81)(75,87)(76,79)(80,83)(82,85)(84,89)(86,88)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=de,f^2=g,g^2=h,b^a=bd,c^a=ch,f^a=fh,c^b=cg,d^b=dh,i^b=i^52,f^c=fh2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84906);