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C₂×#33519 #7622809

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

Aliases

Subgroups

4012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

(1,2);(3,4)(5,6)(7,8)(9,18)(10,15)(11,23)(12,27)(13,16)(14,20)(17,25)(19,34)(21,35)(22,32)(24,29)(26,37)(28,33)(30,36)(31,38);(7,9)(8,14)(10,19)(11,24)(12,28)(13,21)(15,29)(16,30)(17,33)(18,23)(20,25)(22,36)(26,38)(27,31)(32,34)(35,37);(4,6)(7,10,13,12)(8,15,16,27)(9,19,21,28)(11,22,26,25)(14,29,30,31)(17,23,32,37)(18,34,35,33)(20,24,36,38);(8,16)(14,30)(15,27)(17,32)(18,35)(23,37)(29,31)(33,34)

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, 7530005);