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C₂×#24365 #6437643

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

Aliases

Subgroups

4968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344839);