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C₄×#3489 #7625676

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

Aliases

Subgroups

11236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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, 7532872);