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C₂×#3342 #61233

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

Aliases

Subgroups

927 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54221);