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C₂×#61057 #10576067

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

Aliases

Subgroups

10462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 38 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483263);