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C₂²×#2665 #7627731

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

Aliases

Subgroups

8194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

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, 7534927);