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C₂×#3178 #60683

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

Aliases

Subgroups

953 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53671);