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C₂×#61064 #10576075

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

Aliases

Subgroups

10418 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)(9,19,20,33)(10,15,25,32)(11,17,12,16)(14,26,28,22)(21,35,36,30)(23,38,37,29)(24,34,27,31);(7,9,13,20)(8,14,18,28)(10,23,25,37)(11,22,12,26)(15,30,32,35)(16,19,17,33)(21,27,36,24)(29,34,38,31);(4,6)(9,20)(14,28)(19,33)(21,36)(22,26)(23,37)(29,38)(30,35);(7,10)(8,15)(9,21)(11,24)(12,27)(13,25)(14,29)(16,31)(17,34)(18,32)(19,35)(20,36)(22,37)(23,26)(28,38)(30,33);(7,11,13,12)(8,16,18,17)(9,22,20,26)(10,24,25,27)(14,19,28,33)(15,31,32,34)(21,37,36,23)(29,35,38,30)

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, 10483271);