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C₂×#15175 #608436

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

Aliases

Subgroups

4386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(4,6)(7,8,9,10)(13,17)(16,18)(21,25)(24,26);(7,8)(9,10)(12,15)(16,18)(19,20,23,22)(21,26,25,24);(7,8)(9,10)(11,12)(13,16)(14,15)(17,18)(19,21,23,25)(20,24,22,26);(3,4,5,6)(11,13)(12,16)(14,17)(15,18)(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, 515632);