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C₂×#13206 #495118

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

Aliases

Subgroups

1670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402314);