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C₂×#23577 #6432016

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

Aliases

Subgroups

3702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339212);