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C₂×#7959 #181168

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

Aliases

Subgroups

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88364);