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C₂×#13342 #498865

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

Aliases

Subgroups

1586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406061);