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C₂×#23735 #6432412

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

Aliases

Subgroups

3930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339608);