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C₂×#11688 #481442

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

Aliases

Subgroups

1208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 388638);