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C₂×#29386 #6461514

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

Aliases

Subgroups

1868 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6368710);