Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12312 |
372 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 67 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)(57,71)(58,65)(59,67)(61,80)(62,76)(63,77)(64,69)(66,70)(68,72)(73,84)(74,78)(75,79)(81,82)(83,85);(57,70)(58,72)(61,69)(62,74)(64,80)(65,68)(66,71)(73,79)(75,84)(76,78)(81,85)(82,83);(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)(54,55,59,63)(56,64,67,83)(57,69,73,85)(58,74,72,62)(60,75,77,66)(61,79,81,70)(65,80,68,82)(71,76,84,78)Polycyclic presentation:
2^8,53|a^2=h,d^2=f,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,g^a=gh,i^a=i^52,d^b=df,e^b=eg,g^b=gh,d^c=dg,e^c=eg,f^c=fh,g^c=gh788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 82971);