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C₂×#20355 #6369760

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

Aliases

Subgroups

7522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6276956);