Finite Group Databasebeta

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C₂×C₂₃×#485 #15670707

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 49 points:

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1820);