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C₂×#34208 #7625514

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

Aliases

Subgroups

11586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532710);