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C₂×#33774 #7623330

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

Aliases

Subgroups

2014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530526);