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C₂×#27568 #6441058

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

Aliases

Subgroups

2330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6348254);