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C₂×#19852 #6358198

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

Aliases

Subgroups

1893 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265394);