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C₄×#3183 #6373934

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

Aliases

Subgroups

2156 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)(15,19)(16,23)(17,26)(18,21)(20,24)(22,28)(25,27);(6,9)(10,12)(13,15,18,17)(14,19,21,26)(16,24,25,22)(20,27,28,23);(13,16,17,24,18,25,15,22)(14,20,19,23,21,28,26,27);(5,7,8,11)(6,10,9,12)(16,25)(20,28)(22,24)(23,27)

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, 6281130);