Finite Group Databasebeta

?

← Prev (#6630093) Next (#6630095) →

C₂×#33205 #6630094

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

Aliases

Subgroups

2528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6537290);