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C₂×#10873 #353714

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

Aliases

Subgroups

2082 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260910);