Finite Group Databasebeta

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C₂×#61508 #10576804

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

Aliases

Subgroups

6656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484000);