Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C53×#365 ⋊ C2 |
| Sylow | C53 ⋊ #12949 |
394 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 103 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:
(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)(55,63)(57,75)(58,77)(59,71)(60,70)(61,72)(62,79)(64,82)(65,83)(66,84)(67,81)(68,73)(69,74)(76,85)(78,80);(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)(55,62,67,73)(57,74)(58,76)(59,60)(63,79,81,68)(64,66,65,78)(69,75)(70,71)(77,85)(80,82,84,83);(54,55,59,66,61,67,60,78)(56,68,70,82,72,79,71,83)(57,73,76,65,58,62,74,64)(63,75,80,69,81,77,84,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=fg,d^2=g,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,d^b=dg,e^b=eg,f^b=fh,g^b=gh,d^c=dg,e^c=egh,f^c=fh,g^c=gh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86255);