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C₂×#13017 #494513

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

Aliases

Subgroups

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401709);