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C₂×#37972 #7635265

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

Aliases

Subgroups

6384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542461);