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C₂²×#1890 #6371460

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

Aliases

Subgroups

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

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, 6278656);