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C₂×#10909 #353951

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

Aliases

Subgroups

2170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 261147);