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C₂×#61083 #10576106

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

Aliases

Subgroups

10386 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)(9,19,23,34)(10,15,25,32)(11,17,12,16)(14,27,30,22)(20,35,38,29)(21,36,37,28)(24,33,26,31);(7,9,13,23)(8,14,18,30)(10,20,25,38)(11,22,12,27)(15,28,32,36)(16,19,17,34)(21,26,37,24)(29,33,35,31);(4,6)(7,10)(8,15)(9,20)(11,26)(12,24)(13,25)(14,28)(16,33)(17,31)(18,32)(19,35)(21,27)(22,37)(23,38)(29,34)(30,36);(7,10)(8,15)(9,21)(11,24)(12,26)(13,25)(14,29)(16,31)(17,33)(18,32)(19,36)(20,27)(22,38)(23,37)(28,34)(30,35);(7,11,13,12)(8,16,18,17)(9,22,23,27)(10,24,25,26)(14,19,30,34)(15,31,32,33)(20,21,38,37)(28,29,36,35)

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, 10483302);