Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #10119 |
454 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 89 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) = 6784 |
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)(54,56,58,65)(55,60,62,69)(57,67,66,64)(59,63,61,68)(70,73,75,71)(72,79,81,85)(74,84,76,78)(77,80,83,82);(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)(55,59)(56,64)(57,66)(61,62)(63,68)(65,67)(70,72,75,81)(71,77,73,83)(74,82,76,80)(78,85,84,79);(54,55,58,62)(56,63,65,68)(57,59,66,61)(60,67,69,64)(70,71)(72,79)(73,75)(74,84)(76,78)(77,80)(81,85)(82,83)Polycyclic presentation:
2^8,53|a^2=h,b^2=gh,c^2=g,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,c^b=cf,d^b=dg,e^b=eh,f^b=fg,i^b=i^52,d^c=dh,e^c=eh,f^c=fg710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 71125);