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C₂×#4311734 #72294769

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

Aliases

Subgroups

58953 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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