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C₂×#3007 #60358

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

Aliases

Subgroups

2539 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53346);