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C₂×#8197 #182348

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

Aliases

Subgroups

1212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89544);