Finite Group Databasebeta

?

← Prev (#10586248) Next (#10586250) →

C₂×#62908 #10586249

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

Aliases

Subgroups

32484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493445);