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C₂×#24455 #6437825

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

Aliases

Subgroups

5060 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)(13,23)(14,21)(15,18)(16,19)(17,22)(20,24)(25,26);(7,8)(9,10)(11,13,17,24)(12,18,22,26)(14,15,16,25)(19,23,21,20);(4,6)(8,10)(11,14,17,16)(12,19,22,21)(13,15,24,25)(18,23,26,20);(11,15,17,25)(12,20,22,23)(13,14,24,16)(18,21,26,19)

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, 6345021);