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C₂×#12738 #493526

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

Aliases

Subgroups

3274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400722);