Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12507 |
258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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) = 13568 |
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)(54,55,56,58,57,59,60,61)(64,74)(68,82)(72,86)(75,81)(76,90)(83,87)(88,91)(89,93);(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)(62,64,73,89,66,76,79,81,67,74,84,93,78,90,65,75)(63,68,77,88,70,83,85,86,71,82,92,91,80,87,69,72);(55,58)(56,60)(59,61)(62,63,67,71)(64,72,74,86)(65,77,79,92)(66,80,78,70)(68,81,82,75)(69,84,85,73)(76,91,90,88)(83,89,87,93)Polycyclic presentation:
2^8,53|a^2=h,b^2=df,c^2=e,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,c^b=ch,i^c=i^521034 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84240);