Finite Group Databasebeta

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C₂×#1258897 #72334720

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

Aliases

Subgroups

68887 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 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((8,10)(12,15)(16,18)(19,20)(21,24)(22,25)(23,26), (11,12)(13,16)(14,15)(17,18)(19,21)(20,24)(22,26)(23,25), (12,15)(16,18)(21,25)(22,24), (4,6)(8,10)(11,12)(13,16)(14,15)(17,18)(19,21)(20,22)(23,25)(24,26), (3,4,5,6)(7,8,9,10)(11,13,14,17)(12,16,15,18)(19,22)(20,25)(21,26)(23,24), (1,2));