Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #8242 |
384 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 143 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)(70,72,74,81,75,82,73,80)(71,77,78,84,79,85,76,83);(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)(54,56,58,64,57,63,65,69)(55,59,61,67,60,62,66,68)(71,76,79,78)(77,83,85,84);(54,55,57,60)(56,62,63,59)(58,66,65,61)(64,67,69,68)(70,71,74,78,75,79,73,76)(72,77,81,84,82,85,80,83)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=eh,d^2=g,e^2=g,f^2=h,b^a=bd,d^a=dg,f^a=fgh,d^b=dh,i^b=i^521532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 60576);