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C₂²×#2643 #7627720

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

Aliases

Subgroups

9342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4);(5,6,9,10)(7,8,11,12)(14,17)(18,19)(21,22)(23,26)(24,27)(25,28);(6,10)(7,11)(13,14,16,17)(15,18,20,19)(21,23)(22,25)(24,28)(26,27);(5,7)(6,8)(9,11)(10,12)(13,14)(15,19)(16,17)(18,20)(21,23)(22,26)(24,28)(25,27);(5,8)(6,11)(7,10)(9,12)(13,15)(14,18)(16,20)(17,19)(21,22)(23,25)(24,27)(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, 7534916);