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C₂×#30452 #7500766

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

Aliases

Subgroups

4048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7407962);