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C₂×#613881 #72334648

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

Aliases

Subgroups

69247 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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