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C₂×#3284 #61044

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

Aliases

Subgroups

1429 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54032);