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C₂×#521530 #72324053

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

Aliases

Subgroups

74613 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((19,20)(21,23)(22,25)(24,26), (4,6)(11,12,14,15)(13,16,17,18)(19,21)(20,23)(22,26)(24,25), (3,4)(5,6)(7,8,9,10)(12,15)(13,17)(19,21)(20,24)(22,26)(23,25), (11,12)(13,18)(14,15)(16,17)(19,21)(20,23)(22,26)(24,25), (1,2), (11,13)(12,16)(14,17)(15,18)(19,20)(21,24)(22,25)(23,26));