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C₂×#612911 #72299360

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

Aliases

Subgroups

68361 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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