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C₂²×#2747 #7633503

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

Aliases

Subgroups

7250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540699);