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C₂×#23543 #6431960

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

Aliases

Subgroups

4994 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)(13,19)(14,25)(15,20)(16,21)(17,22)(18,23)(24,26);(7,8)(9,10)(11,13)(12,18)(14,15)(16,23)(17,24)(19,20)(21,26)(22,25);(4,6)(8,10)(11,14,15,13,17,23,16,24)(12,19,21,25,22,26,20,18);(11,15,17,16)(12,20,22,21)(13,14,24,23)(18,19,25,26)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339156);