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C₂×#850578 #72337834

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

Aliases

Subgroups

130947 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((7,8,9,10)(11,12,14,16)(13,15,18,17)(19,20)(21,22)(23,24)(25,26), (4,6)(7,8,9,10)(11,12,14,16)(13,17,18,15)(20,24)(22,26), (4,6)(8,10)(13,18)(15,17)(19,21,23,25)(20,22,24,26), (7,8)(9,10)(11,13,14,18)(12,15,16,17)(19,21)(20,22)(23,25)(24,26), (1,2), (3,4)(5,6)(11,12)(13,17)(14,16)(15,18)(19,22)(20,21)(23,26)(24,25));