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C₂×#34642 #7627803

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

Aliases

Subgroups

7546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7534999);