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C₂×#2952 #60166

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

Aliases

Subgroups

1403 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53154);