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C₂×#11245 #358067

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

Aliases

Subgroups

1774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265263);