Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#2873 ⋊ C2 |
| Sylow | C53 ⋊ #10951 |
916 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)(54,57,58,69,59,68,72,83)(55,61,63,67,62,76,70,82)(56,64,71,84,65,80,66,79)(60,73,77,81,75,85,74,78);(54,56)(55,60,62,75)(57,64)(58,71)(59,65)(61,73,76,85)(63,77,70,74)(66,72)(67,81,82,78)(68,80)(69,84)(79,83);(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)(56,60,65,75)(57,67)(58,70)(59,62)(61,69)(63,72)(64,78,80,81)(66,77,71,74)(68,82)(73,84,85,79)(76,83)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=ef,e^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,i^a=i^52,d^b=dh,e^b=eh,f^b=fh,d^c=dh1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75978);