Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #7596 |
406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 13568 |
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)(62,64,66,65)(63,67,68,69)(70,73,74,81)(71,76,77,83)(72,79,80,85)(75,82,78,84);(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)(62,63,66,68)(64,67,65,69)(70,72)(71,75)(73,79)(74,80)(76,82)(77,78)(81,85)(83,84);(54,55,56,58,57,59,60,61)(63,67)(64,65)(68,69)(70,71)(72,78,80,75)(73,76)(74,77)(79,84,85,82)(81,83)Polycyclic presentation:
2^8,53|a^2=e,b^2=g,c^2=f,d^2=g,e^2=h,b^a=bd,c^a=cg,d^a=df,d^b=dg,e^b=efg,i^b=i^521508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57659);