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C₂×#11838 #481945

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

Aliases

Subgroups

715 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 389141);