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C₂²×#2778 #7633520

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

Aliases

Subgroups

10182 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)(13,14,16,17)(15,18,19,20)(21,22)(23,27)(24,25)(26,28);(6,9)(10,12)(14,17)(15,19)(22,25)(23,28);(5,6)(7,10)(8,9)(11,12)(13,14)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28);(5,7,8,11)(6,10,9,12)(13,15)(14,18)(16,19)(17,20)(21,23,24,28)(22,26,25,27)

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, 7540716);