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C₂×#3204 #60748

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

Aliases

Subgroups

1125 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53736);