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C₂×#13170 #495032

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

Aliases

Subgroups

658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,12,17,13,19,28,18)(9,14,11,27,21,16,29,31)(10,22,25,36,26,30,35,37)(15,23,32,38,34,20,33,24);(4,6)(7,9,12,11,13,21,28,29)(8,14,17,27,19,16,18,31)(10,23,25,38,26,20,35,24)(15,22,32,36,34,30,33,37);(7,10,21,23,12,25,29,38,13,26,9,20,28,35,11,24)(8,15,27,37,18,33,14,30,19,34,31,36,17,32,16,22)

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, 402228);