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C₂×#19788 #6358129

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

Aliases

Subgroups

2045 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265325);