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C₂×#17797 #6344318

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

Aliases

Subgroups

2096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251514);