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C₂×C₄×#538 #7625311

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

Aliases

Subgroups

9618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7532507);