Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#3235 ⋊ C2 |
| Sylow | C53 ⋊ #10121 |
544 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 81 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:
(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)(56,61)(57,59)(58,60)(62,65,68,81)(63,70,72,87)(64,74,76,92)(66,80,67,79)(69,83,84,93)(71,89,82,86)(73,90,88,85)(75,78,77,91);(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)(56,60)(58,61)(62,64)(63,69)(65,78)(66,77)(67,75)(68,76)(70,85)(71,88)(72,84)(73,82)(74,80)(79,92)(81,91)(83,86)(87,90)(89,93);(55,58)(56,60)(59,61)(62,63)(64,73)(65,70)(66,82)(67,71)(68,72)(69,75)(74,85)(76,88)(77,84)(78,93)(79,89)(80,86)(81,87)(83,91)(90,92)Polycyclic presentation:
2^8,53|c^2=g,d^2=g,e^2=gh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=egh,c^b=cf,d^b=dg,e^b=eh,f^b=fg,i^b=i^52,d^c=dh,e^c=egh,f^c=fg707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 71139);