Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #10778 |
1164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
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)(54,57)(55,62)(56,67)(58,74)(59,72)(60,73)(61,75)(63,78)(64,79)(65,71)(66,80)(68,84)(69,83)(70,82)(76,81)(77,85);(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)(54,56,59,70,60,69,58,68)(55,61,65,77,63,66,64,76)(57,67,72,82,73,83,74,84)(62,75,71,85,78,80,79,81);(54,55)(56,66,69,61)(57,71,73,79)(58,64)(59,65)(60,63)(62,72,78,74)(67,81)(68,77,70,76)(75,82)(80,84)(83,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^b=fh,i^b=i^52,e^c=eh,f^c=fh1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75062);