Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #13642 |
170 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 95 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)(55,61,60,64)(56,65)(62,76,71,74)(63,75,72,78)(66,79)(67,73)(77,85,82,84)(80,83);(55,60)(56,65)(61,64)(63,72)(66,79)(67,73)(75,78)(80,83);(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)(54,55,56,62,57,63,66,77,58,64,67,76,68,78,80,85,59,60,65,71,69,72,79,82,70,61,73,74,81,75,83,84)Polycyclic presentation:
2^8,53|a^2=e,c^2=d,e^2=f,f^2=g,g^2=h,b^a=bd,c^a=cg,d^a=dh,i^a=i^52,e^b=eh,e^c=eh2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90107);