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C₂²×#2749 #7633524

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

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, 7540720);