Finite Group Databasebeta

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C₂×#35457 #7628825

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

Aliases

Subgroups

6236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536021);