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C₂×#20942 #6371435

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

Aliases

Subgroups

6394 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278631);