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C₂×#24420 #6437981

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

Aliases

Subgroups

4586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,13,9,10,8,14)(5,15,19,24,18,26,16,11)(6,20,21,28,22,12,23,27)(17,29,30,25,31,34,32,33);(4,10)(5,16)(7,8)(11,15)(12,20)(17,30)(18,19)(21,23)(24,26)(25,29)(31,32)(33,34);(3,5)(4,11)(6,17)(7,16)(8,19)(9,18)(10,24)(12,25)(13,26)(14,15)(20,33)(21,32)(22,31)(23,30)(27,29)(28,34);(3,6)(4,12)(5,17)(7,23)(8,21)(9,22)(10,20)(11,25)(13,28)(14,27)(15,29)(16,30)(18,31)(19,32)(24,33)(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, 6345177);