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C₂×#11486 #480127

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

Aliases

Subgroups

988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387323);