Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C53×#362 ⋊ C2 |
| Sylow | C53 ⋊ #13440 |
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(55,57)(58,60,61,72,77,87,79,89,64,75,62,73,63,74,76,88)(59,66,67,82,80,86,78,85,70,84,68,71,69,83,65,81);(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)(59,65)(60,72)(61,76)(62,79)(63,77)(67,69)(68,80)(70,78)(71,85)(73,75)(74,89)(81,82)(83,86)(87,88);(54,55)(56,57)(58,59,64,70)(60,71,75,82)(61,65,62,78)(63,80,77,69)(66,72,84,73)(67,79,68,76)(74,81,87,85)(83,89,86,88)Polycyclic presentation:
2^8,53|a^2=h,c^2=d,d^2=gh,e^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,g^a=gh,c^b=cf,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^52,e^c=eh,f^c=fh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89111);