Finite Group Databasebeta

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C₂×#7693982 #72298748

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

Aliases

Subgroups

At least 7258 conjugacy classes of subgroups; only the 34429 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

214 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((3,4)(5,6)(8,10)(12,14)(13,15)(16,24)(25,26), (3,4,5,6)(7,8)(9,10)(11,12,17,14)(13,18,15,21)(16,19,24,22)(20,25,23,26), (3,4)(5,6)(11,13,17,15)(12,18,14,21)(16,20,24,23)(19,25,22,26), (3,4,5,6)(11,14,17,12)(13,18,15,21)(16,22,24,19)(20,25,23,26), (3,4)(5,6)(11,15,17,13)(12,18,14,21)(16,20,24,23)(19,26,22,25), (11,16)(12,19)(13,20)(14,22)(15,23)(17,24)(18,25)(21,26), (1,2));