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C₂×#23652 #6432196

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

Aliases

Subgroups

2802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339392);