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C₂×#23915 #6437440

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

Aliases

Subgroups

6862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344636);