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C₂×#739698 #72296800

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

Aliases

Subgroups

56189 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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