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C₂²×#2735 #7633502

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

Aliases

Subgroups

13842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540698);