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C₂×#496880 #72314299

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

Aliases

Subgroups

3525 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

112 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)(5,7)(6,9)(8,10)(12,16)(17,24)(18,25)(20,26), (1,2), (3,5,7,4)(6,9,10,8)(12,17,16,24)(13,21)(14,23)(18,20,25,26)(19,22), (3,6,7,10)(4,8,5,9)(12,18)(13,19)(14,23)(16,25)(17,20)(21,22)(24,26), (4,5)(8,9)(11,12,19,17,23,26,22,25,15,16,21,24,14,20,13,18));