Finite Group Databasebeta

?

← Prev (#10586366) Next (#10586368) →

C₂×#63045 #10586367

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

Aliases

Subgroups

36044 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493563);