Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1657 ⋊ C2 |
| Sylow | C53 ⋊ #18994 |
936 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 141 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 — 4 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)(63,70)(68,83)(69,84)(71,78)(72,86)(82,93)(85,87)(88,89);(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)(62,65,67,77)(63,69,70,84)(64,73,75,91)(66,80,81,76)(68,82,83,93)(71,87,78,85)(72,88,86,89)(74,92,79,90);(56,60)(58,61)(62,64)(63,68)(65,73)(66,79)(67,75)(69,82)(70,83)(71,86)(72,78)(74,81)(76,92)(77,91)(80,90)(84,93)(85,88)(87,89);(55,58)(56,60)(59,61)(62,63)(64,72)(65,69)(66,78)(67,70)(68,74)(71,81)(73,89)(75,86)(76,87)(77,84)(79,83)(80,85)(82,90)(88,91)(92,93)Polycyclic presentation:
2^8,53|c^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fgh,e^b=eg,f^b=fh,e^c=eh,f^c=fgh,i^d=i^52554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 150797);