Finite Group Databasebeta

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C₂×#612712 #72334625

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

Aliases

Subgroups

69825 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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