Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #7313 |
470 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 67 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:
(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)(55,60,63,76)(57,69)(58,66,73,84)(59,67)(61,64,68,82)(62,78)(65,71)(70,74,72,83)(75,80)(77,85)(79,81);(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)(56,64,66,81)(57,68,70,79)(59,63,73,80)(60,74,75,69)(61,72,77,71)(65,76,83,78)(67,82,84,85)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=h,b^a=bc,c^a=cf,e^a=egh,f^a=fh,g^a=gh,i^a=i^52,c^b=cg,d^b=dfh,f^b=fh,d^c=dh,e^d=eh860 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56861);