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C₂×#3046 #60421

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

Aliases

Subgroups

1371 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53409);