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C₂×#14392 #520694

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

Aliases

Subgroups

4994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 427890);