Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #12713 |
986 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 986 conjugacy classes of subgroups — too many to draw. Only its 135 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)(55,62)(58,73)(59,75)(61,76)(63,65)(64,66)(67,81)(69,83)(70,85)(72,80)(77,79)(78,82);(54,56,60,71)(55,61,66,79)(57,68,74,84)(58,69,73,83)(59,70,75,85)(62,76,64,77)(63,67,72,82)(65,81,80,78);(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)(54,55,59,65)(56,67,70,76)(57,72,73,62)(58,64,74,63)(60,66,75,80)(61,69,78,84)(68,79,83,81)(71,82,85,77)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,f^b=fg,e^c=eh,f^c=fh,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, 85125);