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C₂×C₄×#454 #6372696

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

Aliases

Subgroups

4740 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)(10,17)(13,21)(14,18)(15,19)(20,22);(7,8)(9,13)(10,18)(11,14)(12,17)(15,20)(16,22)(19,21);(7,9,11,16)(8,13,14,22)(10,19,17,15)(12,20,18,21)

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, 6279892);