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C₂×#2253 #33724

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

Aliases

Subgroups

247 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 42 points:

(1,2);(3,4,6,8)(5,9,10,7)(11,12,14,17)(13,21,23,35)(15,28,26,41)(16,29,27,20)(18,32,30,24)(19,34,31,22)(25,40,39,37)(33,38,36,42);(3,5,6,10)(4,7,8,9)(12,17)(18,30)(19,31)(20,29)(21,35)(28,41)(33,36)(37,40);(11,13,22,38,16,25,26,32,14,23,34,42,27,39,15,24)(12,18,28,37,20,33,31,35,17,30,41,40,29,36,19,21)

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, 26712);