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C₂×#34641 #7627802

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

Aliases

Subgroups

14250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 7534998);