Finite Group Databasebeta

?

← Prev (#7633551) Next (#7633553) →

C₂²×#2795 #7633552

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

Aliases

Subgroups

7770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4);(5,6)(7,11)(8,9)(10,12)(14,15)(18,19)(21,22,24,26)(23,27,28,25);(6,9)(7,12)(13,14,17,15)(16,19,20,18)(21,22)(23,27)(24,26)(25,28);(5,6)(7,10)(8,9)(11,12)(13,15,17,14)(16,19,20,18);(5,7,8,12)(6,10,9,11)(13,16)(14,18)(15,19)(17,20)(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, 7540748);