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C₂×#23888 #6437596

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

Aliases

Subgroups

6091 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344792);