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C₄×#3529 #7625936

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

Aliases

Subgroups

7352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

(1,2,3,4);(5,6)(7,9)(8,10)(11,12)(13,14)(15,21)(16,20)(17,19)(18,22)(23,27)(24,26)(25,28);(5,7)(6,9)(8,11)(10,12)(13,15)(14,18)(16,23)(17,22)(19,21)(20,25)(24,28)(26,27);(6,10)(7,11)(15,22)(18,21)(23,28)(25,27);(6,10)(9,12)(14,19)(15,22)(20,26)(23,28);(13,16,17,24)(14,20,19,26)(15,23,22,28)(18,25,21,27)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533132);