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C₂×#37912 #7635172

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

Aliases

Subgroups

6492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,9)(5,6,8,10)(12,15)(16,18)(19,20,23,21)(22,25,26,24);(3,5)(4,6)(7,8)(9,10)(20,21)(24,25);(3,6)(4,8)(5,9)(7,10)(11,12)(13,16)(14,15)(17,18)(19,21,23,20)(22,25,26,24);(11,13,14,17)(12,16,15,18)(19,22,23,26)(20,24,21,25);(3,6)(4,8)(5,9)(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, 7542368);