Finite Group Databasebeta

?

← Prev (#7633513) Next (#7633515) →

C₂²×#2775 #7633514

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

Aliases

Subgroups

7046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540710);