Finite Group Databasebeta

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C₂×#37675 #7635024

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

Aliases

Subgroups

11162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542220);