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C₂×#23541 #6431958

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

Aliases

Subgroups

5314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339154);