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C₂×#23723 #6432398

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

Aliases

Subgroups

3090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339594);