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C₂×#10570 #241124

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

Aliases

Subgroups

1684 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 148320);