Finite Group Databasebeta

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C₂×#1515118 #72295037

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

Aliases

Subgroups

48027 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

148 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((7,8)(9,10)(11,12,15,13)(14,17,18,16)(19,20)(21,24)(22,23)(25,26), (7,8,9,10)(14,18)(16,17)(20,23)(21,25), (4,6)(7,8)(9,10)(12,13)(14,18)(19,20,22,23)(21,24,25,26), (11,13,15,12)(14,16,18,17)(19,21)(20,24)(22,25)(23,26), (3,4)(5,6)(11,14)(12,16)(13,17)(15,18)(19,20)(21,24)(22,23)(25,26), (1,2));