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C₄×#2368 #513533

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

Aliases

Subgroups

3826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420729);