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C₂×#775187 #72337933

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

Aliases

Subgroups

42355 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

196 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((12,15)(13,17), (3,4,5,6)(20,23)(24,25), (3,4)(5,6)(8,10)(12,15)(13,17)(20,23)(24,25), (4,6)(7,8)(9,10)(11,12,14,15)(13,18,17,16)(19,20)(21,25)(22,23)(24,26), (1,2), (3,4)(5,6)(11,13,14,17)(12,16,15,18)(19,21,22,26)(20,24,23,25));