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C₂×#4414089 #72334447

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

Aliases

Subgroups

73133 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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)(7,8,9,10)(11,12,14,16)(13,15,17,18)(19,20,23,24)(21,22,25,26), (7,8)(9,10)(13,17)(15,18)(21,25)(22,26), (4,6)(8,10)(11,12,14,16)(13,15,17,18)(19,21,23,25)(20,22,24,26), (4,6)(8,10)(11,13)(12,15)(14,17)(16,18)(19,22)(20,21)(23,26)(24,25), (1,2), (3,4)(5,6)(7,8)(9,10)(11,12)(13,18)(14,16)(15,17)(19,20)(21,26)(22,25)(23,24));