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C₂×#13174 #495042

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

Aliases

Subgroups

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402238);