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C₂×#11003 #357558

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

Aliases

Subgroups

4438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,14)(6,18,21,29)(7,22)(8,12)(9,13)(10,16)(11,20,28,19)(15,27,32,24)(17,25)(23,26)(30,31,34,33);(3,5)(4,10)(6,15)(7,23)(8,16)(9,17)(11,27)(12,25)(13,26)(14,22)(18,34)(19,33)(20,31)(21,32)(24,28)(29,30);(3,6)(4,11)(5,15)(7,20)(8,19)(9,21)(10,24)(12,29)(13,28)(14,30)(16,33)(17,32)(18,22)(23,31)(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, 264754);