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C₄×#3179 #6374046

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

Aliases

Subgroups

2102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281242);