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C₂×#7670665 #72302263

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

Aliases

Subgroups

126561 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

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