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C₂×#21100 #6371706

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

Aliases

Subgroups

3262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278902);