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C₂×#34917 #7628084

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

Aliases

Subgroups

6878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 7535280);