Finite Group Databasebeta

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C₂×#60808 #10575512

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

Aliases

Subgroups

8014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482708);