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C₂×#3370 #61312

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

Aliases

Subgroups

975 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54300);