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C₂×#14528 #520983

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

Aliases

Subgroups

5854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 428179);