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C₂×#30294 #6433813

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

Aliases

Subgroups

2206 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)(11,12,14,16)(13,17,18,15)(20,24)(25,26);(4,7)(8,10)(19,20,23,26,22,24,21,25);(3,5)(4,8)(6,9)(7,10)(11,13,14,18)(12,15,16,17)(20,25)(21,23)(24,26);(5,9)(8,10)(19,21,22,23)(20,25,24,26)

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, 6341009);