Finite Group Databasebeta

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C₂×#845785 #72334719

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

Aliases

Subgroups

68605 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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