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C₂×#15075 #608188

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

Aliases

Subgroups

3878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 515384);