Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#1812 ⋊ C2 |
| Sylow | C53 ⋊ #12807 |
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 99 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)(55,61)(58,72)(60,73)(62,76)(63,64)(65,78)(67,83)(69,77)(70,84)(74,75)(79,80)(81,85);(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)(54,56,57,66,59,68,71,82)(55,60,62,65,64,75,69,80)(58,67,70,81,72,83,84,85)(61,73,76,78,63,74,77,79);(54,55)(56,65)(57,69)(58,63,72,61)(59,64)(60,66)(62,71)(67,79,83,78)(68,80)(70,76,84,77)(73,81,74,85)(75,82)Polycyclic presentation:
2^8,53|a^2=f,b^2=d,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,e^c=eh,f^c=fgh,i^c=i^52,f^e=fh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85590);