Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#2230 ⋊ C2 |
| Sylow | C53 ⋊ #12367 |
336 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 61 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)(54,56)(55,60)(57,70)(58,65)(59,66)(61,80)(62,76)(63,77)(64,72)(67,71)(68,83)(69,75)(73,82)(74,78)(79,85)(81,84);(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)(54,55,59,63)(56,60,66,77)(57,69,73,79)(58,74,71,62)(61,68,81,72)(64,80,83,84)(65,78,67,76)(70,75,82,85);(56,64,66,83)(57,68)(58,71)(60,75,77,85)(61,79)(62,74)(65,70,67,82)(69,81)(72,73)(76,80,78,84)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,d^2=f,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=egh,g^a=gh,d^b=df,e^b=eg,g^b=gh,i^b=i^52,d^c=dg,e^c=eg,f^c=fh,g^c=gh626 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83341);