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C₂×#23885 #6437574

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

Aliases

Subgroups

6014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344770);