Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1536 ⋊ C2 |
| Sylow | C53 ⋊ #19054 |
926 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 155 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) = 6784 |
A minimal faithful permutation representation — 4 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)(62,66,68,67)(63,71,72,80)(64,75,76,81)(65,77,79,78)(69,83,84,73)(70,85,86,87)(74,90,91,92)(82,88,93,89);(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)(56,61)(57,59)(58,60)(62,65,68,79)(63,70,72,86)(64,74,76,91)(66,78,67,77)(69,82,84,93)(71,87,80,85)(73,88,83,89)(75,92,81,90);(56,60)(58,61)(62,64)(63,69)(65,74)(66,75)(67,81)(68,76)(70,82)(71,83)(72,84)(73,80)(77,90)(78,92)(79,91)(85,88)(86,93)(87,89);(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)(55,58)(56,60)(59,61)(62,63)(64,73)(65,70)(66,71)(67,80)(68,72)(69,75)(74,89)(76,83)(77,85)(78,87)(79,86)(81,84)(82,90)(88,91)(92,93)Polycyclic presentation:
2^8,53|c^2=g,d^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,e^a=eg,f^a=fgh,i^a=i^52,e^b=eg,f^b=fh,d^c=dg,e^c=eh,f^c=fgh,i^c=i^52710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 151400);