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C₂×#13022 #494524

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

Aliases

Subgroups

1384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401720);