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C₂×#4308012 #72302387

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

Aliases

Subgroups

71709 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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