Finite Group Databasebeta

?

← Prev (#10586272) Next (#10586274) →

C₂×#62930 #10586273

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

Aliases

Subgroups

35300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

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, 10493469);