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C₂×#13338 #498874

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

Aliases

Subgroups

1620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406070);