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C₂×#10000 #235208

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

Aliases

Subgroups

1810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 142404);