Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11917 |
280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 79 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)(54,57,59,71)(55,61,64,63)(56,66,69,68)(58,73,74,70)(60,76,78,65)(62,81,82,79)(67,75,84,72)(77,83,85,80);(54,56)(55,60)(57,66)(58,72)(59,69)(61,76)(62,80)(63,65)(64,78)(67,73)(68,71)(70,84)(74,75)(77,81)(79,85)(82,83);(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)(54,55,58,62,57,63,70,81,59,64,74,82,71,61,73,79)(56,65,67,83,68,60,75,77,69,76,84,80,66,78,72,85)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,d^2=g,e^2=f,f^2=h,b^a=bd,c^a=cg,d^a=df,g^a=gh,i^a=i^52,d^b=dg,e^b=efgh,f^b=fh,e^c=eh,e^d=eh860 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80769);