Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12624 |
456 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 131 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)(54,57,58,63,60,70,72,55)(56,65,67,64,66,77,74,61)(59,69,71,76,73,82,83,62)(68,79,81,78,80,85,84,75);(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)(54,56,59,68)(55,61,62,75)(57,65,69,79)(58,67,71,81)(60,66,73,80)(63,64,76,78)(70,77,82,85)(72,74,83,84);(54,55,58,57,60,63,72,70)(56,64,67,77,66,61,74,65)(59,62,71,69,73,76,83,82)(68,75,81,79,80,78,84,85)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,e^2=h,b^a=bd,c^a=ch,f^a=fg,d^b=dg,g^b=gh,i^b=i^52,f^d=fh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84725);