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C₂×#21306 #6372177

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

Aliases

Subgroups

3750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279373);