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C₂×#60182 #10574153

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

Aliases

Subgroups

10278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 10481349);