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C₂×#11523 #480316

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

Aliases

Subgroups

728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387512);