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C₂×#648065 #72337870

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

Aliases

Subgroups

131517 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

208 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((7,8,10,9)(11,12,15,14)(13,16,18,17)(19,20)(21,24)(22,23)(25,26), (4,6)(7,8,10,9)(11,12,15,14)(13,17,18,16)(20,23)(24,26), (4,6)(7,8)(9,10)(13,18)(16,17)(19,21,22,25)(20,24,23,26), (8,9)(11,13,15,18)(12,16,14,17)(19,21)(20,24)(22,25)(23,26), (1,2), (3,4)(5,6)(7,9,10,8)(11,14,15,12)(13,17,18,16)(19,20)(21,24)(22,23)(25,26));