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C₂×#2116753 #72294362

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

Aliases

Subgroups

49051 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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