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C₂×#14044 #514357

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

Aliases

Subgroups

6890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421553);