Finite Group Databasebeta

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C₂×#72335122 #72335192

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

Aliases

Subgroups

At least 6462 conjugacy classes of subgroups; only the 40120 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

308 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((3,4)(5,6)(12,15)(16,18)(19,20)(21,26)(22,23)(24,25), (4,6)(8,10)(13,17)(16,18)(19,21)(20,22)(23,24)(25,26), (4,6)(8,10)(11,12)(13,18)(14,15)(16,17)(19,22,24,26)(20,23,25,21), (3,4)(5,6)(20,25)(21,23), (1,2), (4,6)(7,8,9,10)(11,12)(13,18)(14,15)(16,17)(19,23,24,21)(20,22,25,26), (3,4)(5,6)(7,8)(9,10)(11,13)(12,16)(14,17)(15,18)(19,22)(20,23)(21,25)(24,26));