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C₂×#12957 #494338

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

Aliases

Subgroups

1066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401534);