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C₄×#1765 #353210

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

Aliases

Subgroups

1890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3,4);(5,6)(7,8)(9,10,13,17,14,18,12,15)(11,16,21,23,19,24,20,22);(6,8)(10,15,18,17)(11,19)(16,23,24,22)(20,21);(9,11,13,21,14,19,12,20)(10,16,17,23,18,24,15,22)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260406);