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C₂×#28174 #6462887

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

Aliases

Subgroups

2552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6370083);