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C₂×#21744 #6374106

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

Aliases

Subgroups

5238 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)(10,12)(11,14)(15,16,18,21,19,22,25,28)(17,20,24,27,23,26,29,30);(7,9)(8,11)(10,14)(12,13)(15,17)(16,20)(18,24)(19,23)(21,27)(22,26)(25,29)(28,30);(4,6)(9,14)(11,13);(8,12)(11,13)(17,23)(20,26)(24,29)(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, 6281302);