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C₂×#34177 #7625419

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

Aliases

Subgroups

8986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532615);