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C₂×#151119 #72320869

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

Aliases

Subgroups

609 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

82 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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