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C₂×#20886 #6371330

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

Aliases

Subgroups

4590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

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, 6278526);