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C₂×#33469 #7622632

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

Aliases

Subgroups

1916 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

(1,2);(4,9,11,24)(5,13)(6,16)(7,20)(10,26,27,34)(12,17,21,25)(14,31)(15,18)(19,22)(23,30,28,29);(3,4)(5,10)(6,17)(7,21)(8,11)(9,22)(12,20)(13,30)(14,27)(15,26)(16,24)(18,34)(19,25)(23,32)(28,33)(29,31);(3,5,7,13,8,14,20,31)(4,10,21,30,11,27,12,29)(6,18,16,33,19,15,22,32)(9,23,17,34,24,28,25,26);(5,14)(10,27)(13,31)(15,18)(23,28)(26,34)(29,30)(32,33)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529828);