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C₂×#15578 #609160

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

Aliases

Subgroups

5790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8,10,9)(11,12)(13,17)(14,15)(16,18)(19,20)(21,22)(23,25)(24,26);(8,9)(12,15)(13,18)(19,21,23,26)(20,22,25,24);(11,12)(13,16)(14,15)(17,18)(19,21)(20,24)(22,25)(23,26);(3,4)(5,6)(7,9,10,8)(11,13,14,18)(12,16,15,17)(19,22,23,24)(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, 516356);