Finite Group Databasebeta

?

← Prev (#10576200) Next (#10576202) →

C₂×#61370 #10576201

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

Aliases

Subgroups

6636 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10483397);