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C₂×#3267 #61025

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

Aliases

Subgroups

1457 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54013);