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C₂×#12918 #494232

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

Aliases

Subgroups

990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401428);