Finite Group Databasebeta

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C₂×#1085253 #72296386

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

Aliases

Subgroups

59211 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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