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C₄×#3485 #7625649

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

Aliases

Subgroups

11450 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)(11,17)(12,20)(13,14)(15,19)(16,21)(18,22)(23,24);(10,14)(15,17)(16,20)(22,23);(5,6)(7,8)(9,11,13,19)(10,15,14,17)(12,18,21,24)(16,22,20,23);(9,10)(11,15)(12,16)(13,14)(17,19)(18,22)(20,21)(23,24);(9,12)(10,16)(11,18)(13,21)(14,20)(15,22)(17,23)(19,24)

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, 7532845);