Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #8509 |
656 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,60,62,67)(59,64,65,73)(61,69,70,66)(63,71,68,72)(74,77,78,75)(76,84,85,81)(79,82,80,83)(86,88,87,89);(58,59)(60,64)(61,68)(62,65)(63,70)(66,71)(67,73)(69,72)(74,76,78,85)(75,81,77,84)(79,87,80,86)(82,89,83,88);(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)(54,55,56,57)(59,63,65,68)(64,72,73,71)(74,75,80,83,78,77,79,82)(76,81,87,89,85,84,86,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=gh,d^2=h,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,i^a=i^52,d^b=dh,e^b=egh,f^b=fgh,d^c=dgh,e^c=eg,f^c=fg1028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62024);