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C₂×#23446 #6431793

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

Aliases

Subgroups

7314 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)(9,13)(10,14)(11,15)(12,16)(17,24)(18,25)(19,26)(20,28)(21,29)(22,30)(23,31)(27,33)(32,36)(34,37)(35,38);(7,9,12,19)(8,13,16,26)(10,17,21,33)(11,22,23,18)(14,27,29,24)(15,30,31,25)(20,34,35,32)(28,36,38,37);(4,6)(7,10)(8,14)(9,17)(11,20)(12,21)(13,24)(15,28)(16,29)(18,32)(19,33)(22,34)(23,35)(25,36)(26,27)(30,37)(31,38);(7,11,12,23)(8,15,16,31)(9,18,19,22)(10,20,21,35)(13,25,26,30)(14,28,29,38)(17,32,33,34)(24,36,27,37)

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, 6338989);