Finite Group Databasebeta

?

← Prev (#6465980) Next (#6465982) →

C₂×#28267 #6465981

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

Aliases

Subgroups

2498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6373177);