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C₂²×#2595 #7628020

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

Aliases

Subgroups

8686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535216);