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C₂×#8475668 #72331978

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

Aliases

Subgroups

59291 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

166 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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