Finite Group Databasebeta

?

← Prev (#6346876) Next (#6346878) →

C₂×#18330 #6346877

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

Aliases

Subgroups

3468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6254073);