Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #12726 |
708 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 127 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)(55,61,63,68)(56,65)(58,69)(59,70)(60,73,74,82)(62,75,71,83)(64,76,77,78)(66,79)(67,80)(72,84)(81,85);(54,56,59,67)(55,60,63,74)(57,65,70,80)(58,66,72,81)(61,73,68,82)(62,64,71,77)(69,79,84,85)(75,76,83,78);(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)(56,64)(57,68)(58,71,72,62)(59,63)(60,66,74,81)(61,70)(65,78)(67,77)(69,75,84,83)(73,85,82,79)(76,80)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=g,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,f^b=fg,e^c=eh,f^d=fh1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85190);