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C₂²×#2570 #7628064

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

Aliases

Subgroups

6698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535260);