Finite Group Databasebeta

?

← Prev (#15670687) Next (#15670689) →

C₂₃×#3069 #15670688

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,30,35)(26,36,38,47)(27,41,43,49)(28,34,29,33)(31,40,46,39)(32,44,48,42)(37,51,52,45)(50,54,55,53);(24,26,28,39,30,38,29,40)(25,31,33,36,35,46,34,47)(27,37,42,53,43,52,44,54)(32,45,41,50,48,51,49,55);(24,27)(25,32)(26,37)(28,42)(29,44)(30,43)(31,45)(33,41)(34,49)(35,48)(36,50)(38,52)(39,53)(40,54)(46,51)(47,55);(26,38)(31,46)(36,47)(37,52)(39,40)(45,51)(50,55)(53,54)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1801);