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C₂×#23423 #6431758

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

Aliases

Subgroups

7922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6338954);