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C₂×#12604 #492944

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

Aliases

Subgroups

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400140);