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C₂×#23992 #6451779

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

Aliases

Subgroups

3784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6358975);