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C₂×#23440 #6431783

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

Aliases

Subgroups

7074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

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, 6338979);