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C₄×#2923 #6369953

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

Aliases

Subgroups

2594 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)(13,14,16,20,17,19,23,26)(15,18,22,25,21,24,27,28);(6,9)(10,12)(13,15)(14,18)(16,22)(17,21)(19,24)(20,25)(23,27)(26,28);(5,7,8,11)(6,10,9,12)(14,19)(18,24)(20,26)(25,28);(15,21)(18,24)(22,27)(25,28)

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, 6277149);