Finite Group Databasebeta

?

← Prev (#7633549) Next (#7633551) →

C₂²×#2790 #7633550

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

Aliases

Subgroups

7554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540746);