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C₂×#20446 #6369907

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

Aliases

Subgroups

3090 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)(18,31,32,37)(21,28)(22,27)(24,29)(25,33,36,35)(34,38);(3,4,5,6)(7,9)(8,13)(10,18)(11,23)(12,20)(14,25)(15,26)(16,30)(17,29)(19,24)(21,32)(22,35)(27,37)(28,36)(31,38)(33,34);(7,10,11,22,12,21,24,34)(8,14,16,27,15,28,29,38)(9,18,23,35,20,32,19,33)(13,25,30,37,26,36,17,31);(8,15)(10,21)(13,26)(16,29)(17,30)(18,32)(22,34)(33,35)

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, 6277103);