Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C53×#349 ⋊ C2 |
| Sylow | C53 ⋊ #12682 |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 points:
(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)(55,57)(60,69)(64,68)(70,72)(71,83)(76,80)(77,82)(84,85)(87,89);(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)(58,60)(59,64)(61,72)(62,71)(63,69)(65,68)(66,80)(67,77)(70,74)(73,85)(75,83)(76,78)(79,82)(81,89)(84,86)(87,88);(54,55)(56,57)(58,59,61,66,62,67,73,81,63,65,74,78,75,79,86,88)(60,68,70,80,71,82,84,89,69,64,72,76,83,77,85,87)Polycyclic presentation:
2^8,53|a^2=f,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=ch,f^b=fh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85008);