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C₂×#12616 #492978

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

Aliases

Subgroups

1118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400174);