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C₂×#664646 #72323873

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

Aliases

Subgroups

73277 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((19,20)(21,26)(22,24)(23,25), (4,6)(8,10)(11,12,14,16)(13,15,18,17)(21,24)(22,26), (7,8)(9,10)(19,21,23,24)(20,22,25,26), (3,4)(5,6)(7,8)(9,10)(11,12)(13,17)(14,16)(15,18)(19,20)(21,22)(23,25)(24,26), (1,2), (3,4)(5,6)(7,8)(9,10)(11,13)(12,15)(14,18)(16,17)(19,22)(20,24)(21,25)(23,26));