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C₂×#23614 #6432132

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

Aliases

Subgroups

3942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339328);