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C₂×#3168 #60670

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

Aliases

Subgroups

1035 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)(11,12)(13,17)(14,21)(15,24)(16,19)(18,22)(20,25)(23,26);(4,7)(8,10)(11,13,16,15)(12,17,19,24)(14,20,23,22)(18,21,25,26);(11,14,15,22,16,23,13,20)(12,18,17,21,19,25,24,26);(3,5,6,9)(4,8,7,10)

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53658);