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C₂×#12642 #493060

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

Aliases

Subgroups

1158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400256);