Finite Group Databasebeta

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C₂×#10321452 #72329331

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

Aliases

Subgroups

At least 9444 conjugacy classes of subgroups; only the 29429 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

166 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((4,7)(8,10)(12,15)(13,17)(19,20)(21,23)(22,25)(24,26), (4,7)(5,9)(11,12)(13,18)(14,15)(16,17)(19,21)(20,23)(22,26)(24,25), (4,7)(5,9)(19,20)(21,24)(22,25)(23,26), (13,17)(16,18)(19,20)(21,23)(22,25)(24,26), (1,2), (3,4,6,7)(5,8,9,10)(11,13)(12,16)(14,17)(15,18), (3,5,6,9)(4,8,7,10)(11,12)(13,18)(14,15)(16,17)(19,21)(20,24)(22,26)(23,25));