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C₂×#782010 #72294323

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

Aliases

Subgroups

56519 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

196 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((11,12,14,16)(13,17,18,15)(19,20,23,25)(21,22,24,26), (11,13)(12,15)(14,18)(16,17)(19,21,23,24)(20,22,25,26), (4,6)(8,10)(12,16)(15,17)(19,22,23,26)(20,21,25,24), (7,8)(9,10)(11,12)(13,15)(14,16)(17,18)(19,20)(21,22)(23,25)(24,26), (3,4)(5,6)(7,8)(9,10)(11,13)(12,17)(14,18)(15,16)(19,22)(20,24)(21,25)(23,26), (1,2));