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C₂×#3040 #60414

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

Aliases

Subgroups

1459 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53402);