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C₂×#23610 #6432129

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

Aliases

Subgroups

3470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339325);