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C₂×#11037 #357594

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

Aliases

Subgroups

4334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264790);