Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C53 ⋊ #8050 |
604 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 151 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) = 3392 |
A minimal faithful permutation representation — 3 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)(54,57,58,65)(55,60,61,67)(56,63,64,69)(59,66,62,68)(72,80)(76,84)(79,85)(81,82);(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)(54,56)(55,59,61,62)(57,63)(58,64)(60,66,67,68)(65,69)(70,72)(71,76,78,84)(73,81)(74,82)(75,80)(77,79,83,85);(54,55)(56,62)(57,60)(58,61)(59,64)(63,68)(65,67)(66,69)(70,71,74,77,75,78,73,83)(72,79,82,84,80,85,81,76)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=h,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fgh,c^b=cg,d^b=dh,i^c=i^521040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 59695);