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C₂×#33381 #7622494

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

Aliases

Subgroups

4120 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)(9,14)(10,13)(11,24)(12,17)(15,21)(16,22)(18,28)(19,25)(20,34)(23,27)(26,35)(29,33)(30,32)(31,36)(37,38);(8,13)(10,21)(11,22)(14,25)(15,16)(17,27)(19,33)(20,32)(23,35)(24,26)(28,36)(29,30)(31,38)(34,37);(7,9)(8,14)(10,19)(11,20)(12,18)(13,25)(15,29)(16,30)(17,28)(21,33)(22,32)(23,31)(24,34)(26,37)(27,36)(35,38);(9,18)(14,28)(19,31)(20,32)(25,36)(29,37)(30,34)(33,38)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529690);