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C₂×#21290 #6372111

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

Aliases

Subgroups

2478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279307);