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C₂×#28224 #6465409

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

Aliases

Subgroups

3106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6372605);