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C₂×#39735 #7637430

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

Aliases

Subgroups

7006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544626);