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C₂×#39199 #7637056

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

Aliases

Subgroups

5890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544252);