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C₂×#30166 #6433488

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

Aliases

Subgroups

2422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6340684);