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C₂×#43360 #7667526

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

Aliases

Subgroups

7834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574722);