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C₂×#10744 #353424

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

Aliases

Subgroups

3990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260620);