Finite Group Databasebeta

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C₂×#10574294 #72233276

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

Aliases

Subgroups

85677 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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