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C₂×#1415 #13613

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

Aliases

Subgroups

171 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6601);