Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C53×#509 ⋊ C2 |
| Sylow | C53 ⋊ #13323 |
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 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)(54,56)(55,62)(57,72)(58,68)(59,65)(60,69)(61,76)(63,80)(64,81)(66,75)(67,74)(70,85)(71,84)(73,83)(77,79)(78,82);(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)(56,66)(57,71)(58,63)(59,75)(60,64)(61,70)(62,68)(65,81)(67,79)(69,80)(72,76)(73,77)(74,82)(78,85)(83,84);(55,61)(56,65)(57,70)(58,59)(62,78)(63,82)(64,77)(66,76)(67,72)(68,69)(71,75)(73,74)(79,80)(81,84)Polycyclic presentation:
2^8,53|d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^a=fh,g^a=gh,c^b=cf,d^b=dg,f^b=fh,g^b=gh,d^c=dh,e^c=eh,f^c=fh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88383);