Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2957 ⋊ C2 |
| Sylow | C53 ⋊ #13032 |
476 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(58,77)(59,71)(60,80)(61,75)(63,82)(64,70)(65,84)(66,73)(68,81)(69,83)(72,79)(74,78)(76,85);(54,56,60,55,61,69,78,65)(57,67,80,62,75,83,74,84)(58,76,59,68,66,63,79,64)(70,77,85,71,81,73,82,72);(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)(54,55,59,64,78,69,58,76,61,65,79,68,60,56,66,63)(57,70,73,62,80,82,72,67,75,81,77,84,74,85,71,83)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,d^2=g,e^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,i^a=i^52,d^b=dg,e^b=eg,f^b=fg,g^b=gh,d^c=dg,e^c=egh,f^c=fg,g^c=gh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86765);