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C₂×#27110 #6446825

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

Aliases

Subgroups

2228 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)(13,17)(14,16)(15,18);(3,5,7,6)(4,8,10,9)(11,13,15,14)(12,16,18,17)(20,23)(21,25)(24,26);(3,5,7,6)(4,9,10,8)(11,14,15,13)(12,17,18,16)(19,20)(21,26)(22,24)(23,25);(3,6,7,5)(4,9,10,8)(12,18)(16,17)(20,24)(23,26)

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, 6354021);