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C₂×#23903 #6437617

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

Aliases

Subgroups

7580 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344813);