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C₂²×#1644 #6348026

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

Aliases

Subgroups

3346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255222);