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C₂×#19294 #6353938

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

Aliases

Subgroups

2024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6261134);