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C₂×#60161 #10574156

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

Aliases

Subgroups

10490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481352);