Finite Group Databasebeta

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C₂×#72334371 #72334730

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

Aliases

Subgroups

At least 8648 conjugacy classes of subgroups; only the 39688 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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