Finite Group Databasebeta

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C₂×#2076529 #72294501

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

Aliases

Subgroups

49921 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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((7,8)(9,10)(11,12,14,15)(13,17,18,16)(19,20,22,24)(21,25,26,23), (7,8,9,10)(12,15)(13,18)(19,20)(21,25)(22,24)(23,26), (4,6)(7,8)(9,10)(11,12)(13,17)(14,15)(16,18)(19,20,22,24)(21,23,26,25), (3,4)(5,6)(7,8)(9,10)(11,12)(13,17)(14,15)(16,18)(19,20)(21,25)(22,24)(23,26), (11,13)(12,16)(14,18)(15,17)(19,21)(20,23)(22,26)(24,25), (1,2));