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C₂×#36166 #7629802

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

Aliases

Subgroups

6396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536998);