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C₂×#3043 #60418

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

Aliases

Subgroups

1429 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53406);