Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C53×#1397 ⋊ C2 |
| Sylow | C53 ⋊ #13723 |
194 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 194 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)(55,59)(58,61)(62,64,65,75,78,88,82,73,68,76,79,90,84,85,70,74,69,77,80,91,92,93,86,89,83,87,81,72,67,71,66,63);(54,56,57,60)(55,58,59,61)(62,63,70,85,67,72,79,76,83,89,82,88,92,91,65,64,69,74,66,71,84,90,81,87,68,73,86,93,78,75,80,77);(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)(63,64)(65,66)(67,78)(68,83)(70,80)(71,75)(72,88)(73,87)(74,77)(76,89)(79,86)(81,82)(84,92)(85,91)(90,93)Polycyclic presentation:
2^8,53|b^2=eh,c^2=d,d^2=fg,e^2=f,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,g^a=gh,i^a=i^52,c^b=ch2126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90555);