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C₂×#60427 #10574973

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

Aliases

Subgroups

10414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8,13,18)(9,14,20,28)(10,23,25,32)(11,17,12,16)(15,26,31,24)(19,33,34,38)(21,30,22,29)(27,36,37,35);(3,4,5,6)(7,9)(8,14)(10,19)(11,21)(12,22)(13,20)(15,27)(16,29)(17,30)(18,28)(23,33)(24,35)(25,34)(26,36)(31,37)(32,38);(7,10)(8,15)(9,19)(11,24)(12,26)(13,25)(14,27)(16,23)(17,32)(18,31)(20,34)(21,35)(22,36)(28,37)(29,33)(30,38);(9,20)(14,28)(19,34)(21,22)(27,37)(29,30)(33,38)(35,36);(7,11,13,12)(8,16,18,17)(9,21,20,22)(10,24,25,26)(14,29,28,30)(15,23,31,32)(19,35,34,36)(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, 10482169);