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C₂×#496836 #72315514

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

Aliases

Subgroups

5439 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

112 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((3,4)(5,8)(6,7)(9,10)(12,16,18,24)(13,19)(17,23,21,25)(20,26), (4,7)(8,10)(12,17)(13,20)(14,22)(16,23)(18,21)(19,26)(24,25), (3,5)(4,8)(6,9)(7,10)(12,18)(16,24)(17,21)(23,25), (1,2), (4,7)(5,9)(11,12,13,21,22,24,26,25,15,18,19,17,14,16,20,23));