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C₂×#2139985 #72297315

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

Aliases

Subgroups

42873 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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