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C₂×#612660 #72334639

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

Aliases

Subgroups

67115 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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