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C₂×#13129 #494847

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

Aliases

Subgroups

758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402043);