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C₂×#3063 #60452

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

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, 53440);