Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2032 ⋊ C2 |
| Sylow | C53 ⋊ #23474 |
1164 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 205 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 — 4 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)(54,58,59,71)(55,62,63,76)(56,65,66,79)(57,69,70,82)(60,73,74,84)(61,75,67,80)(64,78,68,81)(72,83,77,85);(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)(54,57)(55,61)(56,64)(58,69)(59,70)(60,72)(62,75)(63,67)(65,78)(66,68)(71,82)(73,83)(74,77)(76,80)(79,81)(84,85);(54,56)(55,60)(57,68,70,64)(58,65)(59,66)(61,72,67,77)(62,73)(63,74)(69,81,82,78)(71,79)(75,83,80,85)(76,84);(54,55)(56,60)(57,67,70,61)(58,62)(59,63)(64,77,68,72)(65,73)(66,74)(69,80,82,75)(71,76)(78,85,81,83)(79,84)Polycyclic presentation:
2^8,53|a^2=e,b^2=e,d^2=h,b^a=be,c^a=cf,f^a=fh,g^a=gh,c^b=cg,g^b=gh,e^c=eh,i^d=i^52644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 197008);