Finite Group Databasebeta

?

← Prev (#6432597) Next (#6432599) →

C₂×#23808 #6432598

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

Aliases

Subgroups

3298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339794);