Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #8303 |
1050 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 81 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)(55,57)(58,60,62,61)(59,63,65,64)(66,69,70,77)(67,72,73,79)(68,75,76,81)(71,78,74,80);(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)(66,68,70,76)(67,71,73,74)(69,75,77,81)(72,78,79,80);(54,55)(56,57)(58,59,61,64,62,65,60,63)(66,67)(68,74,76,71)(69,72)(70,73)(75,80,81,78)(77,79)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=dg,f^b=fg,i^b=i^521520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 60911);