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C₂×#13387 #499017

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

Aliases

Subgroups

1162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406213);