Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9292 |
426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 107 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) = 3392 |
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)(54,55,59,56)(57,61,58,60)(62,65)(63,69)(64,73)(66,80)(67,78)(68,82)(70,85)(71,76)(72,86)(74,90)(75,89)(77,81)(79,84)(83,92)(87,93)(88,91);(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)(54,56,59,55)(57,60,58,61)(62,64,66,74,67,75,81,91)(63,68,70,72,71,83,79,87)(65,73,80,90,78,89,77,88)(69,82,85,86,76,92,84,93);(54,55,58,61,59,56,57,60)(62,63)(64,72)(65,76,78,69)(66,79)(67,71)(68,74)(70,81)(73,86,89,93)(75,87)(77,84,80,85)(82,88,92,90)(83,91)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=h,d^2=gh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=egh,f^b=fh,d^c=dgh,e^c=eh,f^c=fgh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 66243);