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C₂×#24977 #6447003

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

Aliases

Subgroups

2624 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)(13,15)(14,16)(17,18);(4,7)(8,9)(11,13,14,17)(12,15,16,18)(20,23)(21,25)(24,26);(12,16)(15,18)(19,20)(21,26)(22,24)(23,25);(3,5,6,10)(4,8,7,9)(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, 6354199);