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C₂×#10914 #353971

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

Aliases

Subgroups

1998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261167);