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C₂×#23898 #6437461

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

Aliases

Subgroups

6180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344657);