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C₂×#10872 #353712

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

Aliases

Subgroups

2122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260908);