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C₂×D₄×2₋¹⁺⁴ #10586041

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

Aliases

Subgroups

57140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493237);