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C₂×#10988 #357474

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

Aliases

Subgroups

4382 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)(9,17)(10,21,23,14)(11,24)(12,16)(13,19)(15,27)(18,35,37,34)(20,32)(22,31,26,33)(25,29)(28,38,30,36);(7,9,12,20)(8,13,16,29)(10,18,23,37)(11,25,27,19)(14,30,21,28)(15,32,24,17)(22,38,26,36)(31,35,33,34);(4,6)(7,10)(8,14)(9,18)(11,26)(12,23)(13,28)(15,33)(16,21)(17,34)(19,38)(20,37)(22,27)(24,31)(25,36)(29,30)(32,35)

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, 264670);