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C₂×#12656 #493098

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

Aliases

Subgroups

874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400294);