Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9525 |
538 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 99 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)(55,60)(56,62)(58,65)(59,66)(61,64)(63,68)(67,69)(71,77)(73,74)(76,84)(78,79)(80,85)(81,83);(54,56,58,63)(55,59,61,67)(57,62,65,68)(60,66,64,69)(70,72)(71,76,79,85)(73,81)(74,83)(75,82)(77,84,78,80);(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)(56,59)(57,64,65,60)(58,61)(62,66,68,69)(63,67)(70,71,73,77,75,79,74,78)(72,80,81,76,82,84,83,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=egh,i^a=i^52,e^b=eh,d^c=dh,e^c=eg,f^c=fh1181 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 67629);