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C₂×#3282 #61042

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

Aliases

Subgroups

1467 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(3,4)(5,6)(7,8,11,13)(9,15,18,22)(10,19,20,14)(12,16,21,17);(7,9,11,18)(8,12,13,21)(10,16,20,17)(14,22,19,15);(4,6);(8,13)(9,16)(10,20)(12,15)(17,18)(21,22)

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54030);