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C₂×#36060 #7629479

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

Aliases

Subgroups

14256 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536675);