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C₂×#7137 #126549

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

Aliases

Subgroups

622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 30 points:

(1,2);(3,4)(5,6)(15,16,18,23,19,21,27,28,20,24,26,30,17,22,25,29);(4,6)(7,8,9,11,10,12,13,14)(16,21,24,22)(18,26)(23,29,30,28)(25,27)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 33745);