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C₂×#541 #3453

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

Aliases

Subgroups

502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 2185);