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C₂×#24049 #6440396

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

Aliases

Subgroups

5126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6347592);