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C₂×#3277 #61036

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

Aliases

Subgroups

1381 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 54024);