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C₂×#11685 #481437

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

Aliases

Subgroups

1248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 388633);