Finite Group Databasebeta

?

← Prev (#7635122) Next (#7635124) →

C₂×#37682 #7635123

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

Aliases

Subgroups

12110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542319);