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C₂×#11031 #357585

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

Aliases

Subgroups

4350 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)(9,18)(10,23,26,15)(11,27)(12,16)(13,17)(14,20)(19,31,36,35)(21,30)(22,34)(24,38,37,29)(25,32,28,33);(4,6)(7,9,13,22)(8,14,17,30)(10,24,26,37)(11,21,12,20)(15,31,23,35)(16,34,27,18)(19,28,36,25)(29,32,38,33);(7,10)(8,15)(9,19)(11,25)(12,28)(13,26)(14,29)(16,32)(17,23)(18,35)(20,24)(21,37)(22,36)(27,33)(30,38)(31,34)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264781);