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C₂×#760156 #72296558

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

Aliases

Subgroups

68101 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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