Finite Group Databasebeta

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C₂×#8195808 #72296715

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

Aliases

Subgroups

65197 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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