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C₂×#34211 #7625524

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

Aliases

Subgroups

11842 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)(13,14)(15,23)(16,17)(18,21)(19,24)(20,25)(22,26);(7,9,10,8)(12,17)(14,18)(19,23)(22,25);(3,4,5,6)(11,13)(12,18)(14,17)(15,20)(16,21)(19,25)(22,23)(24,26);(11,14,16,18)(12,13,17,21)(15,22,24,25)(19,20,23,26);(11,15,16,24)(12,19,17,23)(13,20,21,26)(14,22,18,25)

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, 7532720);