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C₂×#24284 #6442581

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

Aliases

Subgroups

5048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6349777);