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C₂×#11507 #480257

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

Aliases

Subgroups

1810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 387453);