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C₂×#23804 #6432593

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

Aliases

Subgroups

3130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339789);