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C₂×#3021 #60385

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

Aliases

Subgroups

2467 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53373);