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C₈×#575 #6344515

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

Aliases

Subgroups

2108 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);(9,10)(11,18)(12,17)(13,21)(14,16)(15,19)(20,24)(22,23);(9,11)(10,15)(12,19)(13,22)(14,20)(16,23)(17,24)(18,21);(10,16)(15,23)(17,21)(18,24);(9,12,14,13)(10,17,16,21)(11,19,20,22)(15,24,23,18)

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, 6251711);