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C₂×#12701 #493377

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

Aliases

Subgroups

3722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400573);