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C₂×#2077550 #72296952

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

Aliases

Subgroups

48197 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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((4,6)(20,23)(24,26), (8,10)(13,17)(16,18)(19,20)(21,24)(22,23)(25,26), (7,8)(9,10)(12,15)(13,17)(20,23)(21,25), (8,10)(11,12)(13,18)(14,15)(16,17)(19,21)(20,24)(22,25)(23,26), (3,4,5,6)(7,8)(9,10)(11,13,14,17)(12,16,15,18)(19,20)(21,24)(22,23)(25,26), (1,2));