Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1946 ⋊ C2 |
| Sylow | C53 ⋊ #13416 |
442 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 95 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)(54,57,58,72,61,76,79,75)(55,63,64,82,66,83,77,71)(56,67,68,85,69,70,65,84)(59,80,78,74,60,81,62,73);(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)(55,62)(57,71)(58,65)(59,77)(60,64)(61,69)(63,75)(66,78)(67,74)(68,79)(70,73)(72,83)(76,82)(80,85)(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)(56,59)(57,70)(58,77)(60,69)(61,66)(62,68)(63,73)(64,79)(65,78)(67,76)(71,80)(72,85)(74,83)(75,84)(81,82)Polycyclic presentation:
2^8,53|c^2=d,d^2=h,e^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,f^a=fgh,g^a=gh,i^a=i^52,c^b=cf,d^b=dh,e^b=egh,f^b=fg,g^b=gh,i^b=i^52,e^c=egh,f^c=fgh,g^c=gh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88965);