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C₂×#732472 #72325293

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

Aliases

Subgroups

71713 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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)(13,16)(14,15)(17,18)(19,20)(21,22)(23,24)(25,26), (3,4)(5,6)(20,24)(21,25), (12,14)(16,18), (4,6)(7,8,9,10)(11,13,15,17)(12,16,14,18)(19,21,23,25)(20,22,24,26), (1,2), (3,4)(5,6)(7,8)(9,10)(11,14,15,12)(13,16,17,18)(19,22)(20,21)(23,26)(24,25));