Finite Group Databasebeta

?

← Prev (#10578608) Next (#10578610) →

C₂×#61932 #10578609

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

Aliases

Subgroups

6762 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

(1,2);(3,4)(5,13)(6,10)(7,11)(8,12)(9,15)(14,18)(16,17)(19,20)(21,31)(22,26)(23,30)(24,29)(25,28)(27,33)(32,34);(3,5,8,15)(4,9,12,13)(6,14,7,16)(10,17,11,18)(19,21,24,22)(20,26,29,31)(23,33,25,32)(27,30,34,28);(3,6,8,7)(4,10,12,11)(5,14,15,16)(9,17,13,18)(19,22,24,21)(20,27,29,34)(23,33,25,32)(26,30,31,28);(3,7,8,6)(4,11,12,10)(5,14,15,16)(9,17,13,18);(4,12)(9,13)(10,11)(17,18)(19,23,24,25)(20,28,29,30)(21,32,22,33)(26,34,31,27)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485805);