Finite Group Databasebeta

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C₂×#35546 #7628926

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

Aliases

Subgroups

6482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536122);