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C₂×#22072 #6375582

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

Aliases

Subgroups

2378 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)(15,16,20,17,19,22,28,24)(18,21,27,23,26,29,30,25);(8,11)(9,13)(15,17,20,22,19,24,28,16)(18,25,27,21,26,23,30,29);(4,6)(7,9,10,13)(8,12,11,14)(15,18,19,26)(16,21,22,29)(17,23,24,25)(20,27,28,30);(8,11)(12,14)(16,22)(17,24)(18,26)(27,30)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6282778);