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C₂×#9105 #196240

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

Aliases

Subgroups

1704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(3,4,7,9,6,5,8,10)(11,12)(13,19)(14,22,24,17)(15,21)(16,18)(20,23,26,25);(3,5,7,10,6,4,8,9)(11,13,19,12,16,21,15,18)(14,20,23,17,24,26,25,22);(4,5)(9,10)(11,14)(12,17)(13,20)(15,25)(16,24)(18,22)(19,23)(21,26)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 103436);