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C₄×#3267 #6383906

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

Aliases

Subgroups

2850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6291102);