Finite Group Databasebeta

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C₂×#613437 #72302739

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

Aliases

Subgroups

71233 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((1,2)(8,10)(11,12,15,13)(14,16,18,17), (4,6)(8,10)(11,12,15,13)(14,16,18,17)(20,23)(24,25), (3,4)(5,6)(7,8,9,10)(14,18)(16,17)(19,20)(21,24)(22,23)(25,26), (3,4)(5,6)(7,8)(9,10)(11,12,15,13)(14,17,18,16)(19,21,22,26)(20,24,23,25), (3,4)(5,6)(7,8)(9,10)(11,13,15,12)(14,16,18,17)(19,20)(21,24)(22,23)(25,26), (11,14)(12,16)(13,17)(15,18)(19,21)(20,25)(22,26)(23,24));