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C₂×#10990 #357477

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

Aliases

Subgroups

4390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264673);