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C₂×#60370 #10574865

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

Aliases

Subgroups

22042 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 38 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482061);