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C₂×#19980 #6358370

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

Aliases

Subgroups

1840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265566);