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C₂×#13119 #494814

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

Aliases

Subgroups

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402010);