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C₂×#33858 #7623658

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

Aliases

Subgroups

1970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530854);