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C₂×C₄×#472 #6372907

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

Aliases

Subgroups

2868 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 6280103);