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C₂×#12817 #493771

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

Aliases

Subgroups

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400967);