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C₂×#33471 #7622634

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

Aliases

Subgroups

1986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529830);