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C₂×#22209 #6376229

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

Aliases

Subgroups

2466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6283425);