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C₂×#10750 #353436

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

Aliases

Subgroups

4306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 260632);