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C₂×#23031 #6381931

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

Aliases

Subgroups

3118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6289127);