Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1630 ⋊ C2 |
| Sylow | C53 ⋊ #18719 |
928 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 149 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:
(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)(62,66,68,67)(63,71,73,72)(64,76,77,81)(65,78,79,80)(69,74,83,87)(70,84,85,86)(75,89,91,90)(82,92,93,88);(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)(62,65,68,79)(63,70,73,85)(64,75,77,91)(66,80,67,78)(69,82,83,93)(71,86,72,84)(74,88,87,92)(76,90,81,89);(56,60)(58,61)(62,64)(63,69)(65,75)(66,76)(67,81)(68,77)(70,82)(71,74)(72,87)(73,83)(78,89)(79,91)(80,90)(84,92)(85,93)(86,88);(55,58)(56,60)(59,61)(62,63,68,73)(64,74,77,87)(65,70,79,85)(66,72,67,71)(69,81,83,76)(75,88,91,92)(78,86,80,84)(82,89,93,90)Polycyclic presentation:
2^8,53|a^2=g,c^2=g,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,e^b=eg,f^b=fh,d^c=dg,e^c=eh,f^c=fh,i^d=i^52716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 147744);