Finite Group Databasebeta

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C₂×#4312055 #72325406

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

Aliases

Subgroups

58277 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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