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C₂×#1445 #13845

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

Aliases

Subgroups

1471 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6833);