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C₂×#23401 #6431721

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

Aliases

Subgroups

7218 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)(9,17)(10,14)(11,23)(12,16)(13,19)(15,26)(18,34)(20,32)(21,30)(22,33)(24,28)(25,31)(27,37)(29,36)(35,38);(7,9,12,20)(8,13,16,28)(10,18,21,35)(11,24,26,19)(14,29,30,27)(15,32,23,17)(22,37,25,36)(31,38,33,34);(4,6)(7,10)(8,14)(9,18)(11,25)(12,21)(13,27)(15,33)(16,30)(17,34)(19,37)(20,35)(22,26)(23,31)(24,36)(28,29)(32,38);(10,21)(14,30)(18,35)(22,25)(27,29)(31,33)(34,38)(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, 6338917);