Finite Group Databasebeta

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C₂×#7686802 #72298737

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

Aliases

Subgroups

At least 7116 conjugacy classes of subgroups; only the 34445 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

226 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((8,10)(14,21)(17,25)(19,22)(23,26), (3,4,5,6)(7,8)(9,10)(11,12)(13,16)(14,17)(15,18)(19,23)(20,24)(21,25)(22,26), (3,4)(5,6)(11,12,15,18)(13,16,20,24)(14,17,21,25)(19,23,22,26), (4,6)(11,12)(13,16)(14,17)(15,18)(19,23)(20,24)(21,25)(22,26), (3,4)(5,6)(11,13,15,20)(12,16,18,24)(14,22,21,19)(17,26,25,23), (11,14)(12,17)(13,19)(15,21)(16,23)(18,25)(20,22)(24,26), (1,2));