Finite Group Databasebeta

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C₂×#4379719 #72324416

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

Aliases

Subgroups

66241 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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