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C₂×C₃×#2684 #10670711

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

4270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 25 points:

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

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 45092);