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C₂×#8739 #190041

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

Aliases

Subgroups

1992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 97237);