Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1670 ⋊ C2 |
| Sylow | C53 ⋊ #12335 |
312 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 67 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:
(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)(54,55,57,59)(56,61,60,58)(62,65,68,67)(63,70,72,82)(64,74,76,83)(66,77,81,80)(69,85,87,86)(71,78,89,90)(73,91,92,88)(75,79,84,93);(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)(56,60)(58,61)(62,64,68,76)(63,69,72,87)(65,74,67,83)(66,79,81,93)(70,85,82,86)(71,88,89,91)(73,90,92,78)(75,77,84,80);(55,58)(56,60)(59,61)(62,63,68,72)(64,73,76,92)(65,70,67,82)(66,78,81,90)(69,84,87,75)(71,77,89,80)(74,91,83,88)(79,85,93,86)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,c^2=gh,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,d^b=df,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=eg794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83123);