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C₂×#20933 #6371414

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

Aliases

Subgroups

6958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(4,6)(7,8)(9,10)(11,12,15,18,16,19,14,20)(13,21,24,17,22,25,23,26);(3,4,5,6)(11,13)(12,17)(14,24)(15,23)(16,22)(18,21)(19,26)(20,25);(8,10)(12,18)(14,15)(17,21)(19,20)(23,24)(25,26);(12,19)(13,22)(18,20)(23,24)

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, 6278610);