Finite Group Databasebeta

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C₂×#617115 #72297029

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

Aliases

Subgroups

42251 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((7,8)(9,10)(11,12,14,16)(13,17,18,15)(19,20,22,24)(21,25,26,23), (7,8,9,10)(13,18)(15,17)(19,20,22,24)(21,25,26,23), (8,10)(21,26)(23,25), (4,6)(7,8)(9,10)(11,12)(13,15)(14,16)(17,18)(19,21)(20,23)(22,26)(24,25), (3,4)(5,6)(11,13)(12,15)(14,18)(16,17)(19,20)(21,23)(22,24)(25,26), (1,2));