Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11537 |
348 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 91 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)(54,56,58,66,59,67,71,83)(55,61,74,79,60,72,63,64)(57,68,70,75,69,65,81,82)(62,77,85,80,73,76,78,84);(55,60)(61,72)(63,74)(64,79);(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)(54,55,57,62,58,63,70,78,59,60,69,73,71,74,81,85)(56,64,65,80,66,72,82,77,67,79,68,84,83,61,75,76)Polycyclic presentation:
2^8,53|a^2=e,c^2=fg,e^2=g,g^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^52,e^b=ef,e^c=eh,e^d=eh1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79068);