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C₄×#3357 #6384702

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

Aliases

Subgroups

1998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6291898);