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C₂×#20510 #6370085

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

Aliases

Subgroups

3050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6277281);