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C₂×#13125 #494835

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

Aliases

Subgroups

804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402031);