Finite Group Databasebeta

?

← Prev (#6438008) Next (#6438010) →

C₂×#24409 #6438009

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

Aliases

Subgroups

4602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6345205);