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C₂×#19654 #6357146

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

Aliases

Subgroups

2346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6264342);