Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#413 ⋊ C2 |
| Sylow | C53 ⋊ #23525 |
1332 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)(54,58,60,59)(55,63,65,64)(56,68,70,69)(57,73,75,74)(61,66,77,81)(62,71,80,79)(67,83,72,84)(76,82,78,85);(54,57,58,73,60,75,59,74)(55,62,64,79,65,80,63,71)(56,67,69,84,70,72,68,83)(61,76,66,82,77,78,81,85);(54,56)(55,61)(57,72)(58,68)(59,69)(60,70)(62,78)(63,66)(64,81)(65,77)(67,75)(71,85)(73,84)(74,83)(76,80)(79,82);(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)(54,55)(56,66)(57,71)(58,63)(59,64)(60,65)(61,69)(62,74)(67,78)(68,77)(70,81)(72,76)(73,80)(75,79)(82,84)(83,85)Polycyclic presentation:
2^8,53|c^2=e,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^52,c^b=cg,e^b=eh,g^c=gh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 197414);