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C₂×#60048 #7667074

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

Aliases

Subgroups

8170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7574270);