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C₂×#23661 #6432213

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

Aliases

Subgroups

2574 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)(9,14)(10,12)(11,13)(15,16)(17,20)(18,22)(19,21)(23,27)(24,29)(25,28)(26,30);(7,9,11,10)(8,12,13,14)(15,17,19,25)(16,20,21,28)(18,23,26,24)(22,27,30,29);(4,6)(7,10,11,9)(8,12,13,14)(17,23)(18,26)(20,27)(22,30)(24,25)(28,29);(16,21)(20,28)(22,30)(27,29)

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, 6339409);