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C₂×#36018 #7629660

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

Aliases

Subgroups

11498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536856);