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C₂×#60324 #10574484

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

Aliases

Subgroups

6884 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10481680);