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C₂×#24399 #6437787

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

Aliases

Subgroups

5114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344983);