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C₂×#21321 #6372201

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

Aliases

Subgroups

3794 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)(9,13)(10,11)(12,14)(15,16)(17,24)(18,22)(19,28)(20,23)(21,27)(25,30)(26,29);(4,6)(8,11)(12,13)(15,17,19,27,20,25,18,26)(16,21,22,24,23,29,28,30);(7,9,10,14)(8,12,11,13)(17,25)(21,29)(24,30)(26,27);(15,18,20,19)(16,22,23,28)(17,26,25,27)(21,24,29,30)

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, 6279397);