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C₂×#23609 #6432126

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4,5,6)(11,12)(13,22)(14,23)(15,19)(16,20)(17,21)(18,25)(24,26);(7,8)(9,10)(11,13,15,23,17,18,16,24)(12,14,20,22,21,26,19,25);(4,6)(8,10)(11,14)(12,18)(13,21)(15,25)(16,22)(17,26)(19,24)(20,23);(11,15,17,16)(12,19,21,20)(13,23,18,24)(14,25,26,22)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339322);