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C₂×#30189 #6433719

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

Aliases

Subgroups

2682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6340915);