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C₂²×#2577 #7628012

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

Aliases

Subgroups

7642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4);(5,6,8,9)(7,11,12,10)(13,14,17,16)(15,19,20,18)(23,27)(26,28);(6,9)(10,11)(15,20)(18,19)(21,22,25,24)(23,26,27,28);(5,6)(7,10)(8,9)(11,12)(13,15)(14,18)(16,19)(17,20)(21,23)(22,26)(24,28)(25,27);(5,7)(6,10)(8,12)(9,11)(13,16,17,14)(15,19,20,18)(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, 7535208);