Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C53 ⋊ #33299 |
662 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 235 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) = 13568 |
A minimal faithful permutation representation — 4 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)(55,59)(58,61)(70,73,74,82,75,83,81,72)(71,78,79,76,77,80,84,85);(62,64,65,69)(63,66,67,68)(71,77)(72,82)(73,83)(79,84);(54,56,57,60)(55,58,59,61)(70,72,81,83,75,82,74,73)(71,76,84,78,77,85,79,80);(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)(56,58)(57,59)(60,61)(62,63,65,67)(64,68,69,66)(70,71,75,77)(72,80,82,78)(73,76,83,85)(74,84,81,79)Polycyclic presentation:
2^8,53|a^2=f,b^2=gh,c^2=fh,d^2=e,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,g^a=gh,i^a=i^52,c^b=ch,d^c=dh2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322080);