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C₂×#10759 #353325

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

Aliases

Subgroups

4138 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)(9,19)(10,24,26,15)(11,18)(12,16)(13,17)(14,21)(20,34,36,33)(22,29)(23,30)(25,31,27,32)(28,35,38,37);(4,6)(7,9,12,22,13,23,11,21)(8,14,18,30,17,29,16,19)(10,20,27,37,26,36,25,35)(15,28,32,34,24,38,31,33);(7,10)(8,15)(9,20)(11,25)(12,27)(13,26)(14,28)(16,31)(17,24)(18,32)(19,33)(21,35)(22,37)(23,36)(29,38)(30,34)

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, 260521);