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C₄×#3322 #6384122

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

Aliases

Subgroups

2334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6291318);