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C₂×#60422 #10574949

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

Aliases

Subgroups

10522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482145);