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C₂×#21021 #6371568

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

Aliases

Subgroups

2626 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)(15,16,18,22,19,21,25,28)(17,20,24,27,23,26,29,30);(8,11)(12,14)(15,17,18,24,19,23,25,29)(16,20,22,27,21,26,28,30);(4,6)(7,9,10,13)(8,12,11,14)(17,23)(20,26)(24,29)(27,30);(16,21)(20,26)(22,28)(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, 6278764);