Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12892 |
274 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 93 points:
(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)(55,59)(58,61)(62,65,66,81,85,78,67,80,69,83,87,79,68,82,86,64)(63,71,72,91,74,93,73,70,76,77,88,90,75,89,84,92);(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)(54,56,57,60)(55,58,59,61)(62,64,67,78,68,79,66,65,69,80,86,82,85,81,87,83)(63,70,73,89,75,91,72,77,76,92,84,93,74,90,88,71);(54,55)(56,58)(57,59)(60,61)(62,63,68,74,69,76,85,75)(64,77,79,89,80,71,81,93)(65,70,82,90,83,92,78,91)(66,84,86,72,87,73,67,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=e,c^2=d,d^2=gh,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,g^a=gh,c^b=ch,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85959);