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C₂×#23666 #6432226

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

Aliases

Subgroups

2698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339422);