Finite Group Databasebeta

?

← Prev (#6432021) Next (#6432023) →

C₂×#23581 #6432022

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

Aliases

Subgroups

3622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339218);