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C₂²×#1829 #6370899

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

Aliases

Subgroups

5066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278095);