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C₂×#8266 #183334

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

Aliases

Subgroups

1014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 90530);