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C₂×#3489 #62801

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

Aliases

Subgroups

5719 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55789);