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C₂×#31224 #7503791

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

Aliases

Subgroups

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7410987);