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C₂×#23873 #6437583

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

Aliases

Subgroups

6084 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344779);