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C₂×#33611 #7622971

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

Aliases

Subgroups

1986 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)(11,25)(12,24)(13,17)(14,21)(16,26)(19,31)(20,32)(22,38)(23,34)(27,28)(29,35)(30,37)(33,36);(7,9,19,35,12,22,11,21,13,23,26,36,10,20,27,37)(8,14,28,38,15,29,16,18,17,30,25,32,24,33,31,34);(4,6)(7,8)(9,14)(10,24)(11,16)(12,15)(13,17)(18,21)(19,28)(20,33)(22,29)(23,30)(25,26)(27,31)(32,36)(34,37)(35,38);(7,10,13,12)(8,15,17,24)(9,20,23,22)(11,19,27,26)(14,29,30,33)(16,25,31,28)(18,32,34,38)(21,35,37,36)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530167);