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C₂×#36687 #7633404

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

Aliases

Subgroups

8898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540600);