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C₂×#20444 #6369905

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

Aliases

Subgroups

3114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277101);