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C₂×#26062 #6443424

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

Aliases

Subgroups

2326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

(1,2);(7,8,10,12)(9,13,14,11)(15,16,20,22)(17,25,18,28)(19,30,26,24)(21,29,23,27);(3,4)(5,6)(15,17,19,27,20,18,26,29)(16,21,24,25,22,23,30,28);(4,6)(7,9,10,14)(8,11,12,13)(16,22)(21,23)(24,30)(25,28);(15,18,19,29,20,17,26,27)(16,23,24,28,22,21,30,25)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6350620);