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C₂×#17788 #6344307

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

Aliases

Subgroups

2164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251503);