Finite Group Databasebeta

?

← Prev (#6437580) Next (#6437582) →

C₂×#23874 #6437581

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

Aliases

Subgroups

6052 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344777);