Finite Group Databasebeta

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C₂×#845310 #72323973

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

Aliases

Subgroups

131363 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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