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C₂×#37651 #7635023

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

Aliases

Subgroups

11672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542219);