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C₂×#2710 #52132

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

Aliases

Subgroups

1555 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45120);