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C₂²×#2618 #7627712

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

Aliases

Subgroups

14546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

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, 7534908);