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C₂×#1416 #13614

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

Aliases

Subgroups

151 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 38 points:

(1,2);(3,4,5,6)(8,13)(9,17)(10,19)(11,23)(14,29)(15,32)(16,28)(18,22)(20,36)(21,26)(24,30)(25,27)(31,37)(33,34)(35,38);(7,8,12,16)(9,18,21,35)(10,22,24,38)(11,25,23,15)(13,26,28,17)(14,30,31,19)(20,37,33,29)(27,34,32,36)

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6602);