Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13374 |
360 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 360 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)(54,56)(55,60)(57,70)(58,74)(59,66)(61,77)(62,65)(63,79)(64,80)(67,84)(68,75)(69,81)(71,83)(72,85)(73,76)(78,82);(54,55)(56,65,66,60)(57,61)(58,63)(59,62)(64,67,81,83)(68,79,74,76)(69,71)(70,82,85,77)(72,78)(73,75)(80,84);(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)(56,64,66,81)(57,69)(58,73)(59,62)(60,67,65,83)(61,71)(63,75)(68,77,74,82)(70,79,85,76)(72,80)(78,84)Polycyclic presentation:
2^8,53|a^2=d,b^2=d,e^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,g^a=gh,i^a=i^52,c^b=cf,f^b=fh,d^c=dh,e^c=egh,g^c=gh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88691);