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C₂×#8417 #186185

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

Aliases

Subgroups

2264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(4,7,8,9)(11,12,15,20,17,14,16,19)(13,21,24,22,25,26,23,18);(3,4)(5,9)(6,8)(7,10)(11,13)(12,18)(14,22)(15,24)(16,23)(17,25)(19,26)(20,21);(11,14,17,12)(13,22,25,18)(15,20,16,19)(21,23,26,24)

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 93381);