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C₂×#21692 #6373728

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

Aliases

Subgroups

3782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(4,6)(7,8,10,9)(12,15)(13,16)(17,18);(11,12,16,18,14,17,13,15);(3,4,5,6);(7,9,10,8)(12,17)(15,18)

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, 6280924);