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C₂×#13164 #495017

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

Aliases

Subgroups

676 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402213);