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C₂×#18774 #6348689

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

Aliases

Subgroups

3332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255885);