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C₂×#60175 #10574164

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

Aliases

Subgroups

10306 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)(9,17)(10,15)(11,23)(12,14)(13,19)(16,25)(18,31)(20,30)(21,28)(22,35)(24,26)(27,33)(29,34)(32,38)(36,37);(7,9,12,20)(8,13,14,26)(10,18,21,32)(11,24,25,19)(15,27,28,37)(16,30,23,17)(22,36,34,33)(29,38,35,31);(3,5,6,4)(8,14)(13,26)(15,28)(16,23)(17,30)(27,37)(29,35)(31,38);(7,10)(8,15)(9,18)(11,22)(12,21)(13,27)(14,28)(16,29)(17,31)(19,33)(20,32)(23,35)(24,36)(25,34)(26,37)(30,38);(10,21)(15,28)(18,32)(22,34)(27,37)(29,35)(31,38)(33,36)

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481360);