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C₂×#152139 #72292709

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

Aliases

Subgroups

4651 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 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((4,9)(12,24)(26,34)(27,32), (1,2), (4,10,9,22)(5,13)(7,20)(11,27,23,32)(12,29,24,16)(14,31)(15,21)(17,25)(19,33)(26,30,34,28), (3,4,5,11,8,9,15,23)(6,16,17,32,18,29,14,27)(7,12,21,30,20,24,13,28)(10,25,26,19,22,31,34,33));