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C₂×#38144 #7635404

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

Aliases

Subgroups

6706 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542600);