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C₂×#2108812 #72325555

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

Aliases

Subgroups

42499 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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