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C₂×#25084 #6438732

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

Aliases

Subgroups

3970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345928);