Finite Group Databasebeta

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C₂×#8598937 #72337801

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

Aliases

Subgroups

At least 9646 conjugacy classes of subgroups; only the 29509 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

178 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)(21,25)(23,26), (4,7)(5,9)(12,15)(13,17)(19,20,22,24)(21,26,25,23), (5,9)(8,10)(19,20)(21,26)(22,24)(23,25), (4,7)(8,10)(13,17)(16,18), (1,2), (3,4,6,7)(5,8,9,10)(11,12)(13,16)(14,15)(17,18)(19,21)(20,23)(22,25)(24,26), (3,5,6,9)(4,8,7,10)(11,13,14,17)(12,16,15,18));