Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C53 ⋊ #20370 |
908 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 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)(57,68)(61,73)(65,78)(69,81)(71,82)(74,83)(76,84)(79,85);(54,57,58,69,59,68,70,81)(55,61,62,74,63,73,75,83)(56,65,66,79,67,78,80,85)(60,71,64,76,72,82,77,84);(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)(54,56)(55,60,63,72)(57,65)(58,66)(59,67)(61,71,73,82)(62,64,75,77)(68,78)(69,79)(70,80)(74,76,83,84)(81,85);(54,55)(56,64,67,77)(57,61)(58,62)(59,63)(60,66,72,80)(65,76,78,84)(68,73)(69,74)(70,75)(71,79,82,85)(81,83)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=e,e^2=h,b^a=be,g^a=gh,f^b=fh,i^b=i^52,d^c=dh1850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 167075);