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C₂×#23421 #6431750

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

Aliases

Subgroups

7682 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)(14,19)(15,20)(16,21)(17,24)(18,23)(25,26);(4,6)(7,8)(9,10)(11,13)(12,17)(14,23)(15,24)(16,25)(18,21)(19,22)(20,26);(8,10)(11,13)(12,18)(14,23)(15,24)(16,25)(17,21)(19,26)(20,22);(11,14,16,15)(12,19,21,20)(13,23,25,24)(17,22,18,26)

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, 6338946);