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C₂×#21240 #6372014

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

Aliases

Subgroups

5066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279210);