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C₂×#4414325 #72334627

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

Aliases

Subgroups

82395 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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