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C₂×#12671 #493139

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

Aliases

Subgroups

746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

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, 400335);