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C₂²×#2807 #7633589

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

Aliases

Subgroups

7554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540785);