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C₂×#39567 #7636821

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

Aliases

Subgroups

6416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 7544017);