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C₂×#24398 #6437786

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

Aliases

Subgroups

5200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,6)(7,8,11,15,10,14,20,13)(9,16,17,22,18,12,19,21);(4,6)(7,9)(8,12)(10,18)(11,17)(13,22)(14,16)(15,21)(19,20);(8,13)(9,17)(11,20)(14,15)(18,19)(21,22);(4,6)(8,14)(12,16)(13,15)(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, 6344982);