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C₂×#21072 #6371660

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

Aliases

Subgroups

3226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278856);