Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7272 |
208 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 107 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 — 2 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)(54,56,58,68,71,67,81,82,59,69,73,83,57,66,70,80)(55,60,63,75,62,65,78,79,61,76,77,85,64,74,72,84);(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)(54,55,57,62,59,61,71,64)(56,65,67,60,69,74,66,76)(58,72,70,63,73,78,81,77)(68,75,82,84,83,85,80,79)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fh,d^2=h,e^2=fg,g^2=h,b^a=bc,c^a=cf,e^a=efgh,g^a=gh,c^b=cg,d^b=dh,f^b=fh,g^b=gh,i^b=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56749);