Finite Group Databasebeta

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C₂×#61827 #10578223

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

Aliases

Subgroups

7244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485419);