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C₂×#12606 #492950

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

Aliases

Subgroups

1286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400146);