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C₂×#28144 #6462787

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

Aliases

Subgroups

2910 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)(17,23)(18,21)(19,22)(20,26)(24,28)(25,30)(27,29);(8,11)(12,13)(15,17,24,25,18,26,19,27)(16,20,28,29,21,23,22,30);(4,6)(17,25)(19,24)(20,29)(22,28)(23,30)(26,27);(7,9,10,14)(8,12,11,13)(16,21)(20,23)(22,28)(29,30)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6369983);