Finite Group Databasebeta

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C₂×#72334364 #72334727

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

Aliases

Subgroups

At least 6848 conjugacy classes of subgroups; only the 40488 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

344 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)(8,10)(11,12,15,17)(13,18,16,14)(19,20,22,24)(21,25,26,23), (11,13)(12,14)(15,16)(17,18)(19,20)(21,23)(22,24)(25,26), (13,16)(14,18)(19,21)(20,23)(22,26)(24,25), (4,6)(7,8,9,10)(11,14,15,18)(12,16,17,13)(19,20)(21,25)(22,24)(23,26), (7,8)(9,10), (1,2), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,17)(16,18)(19,21)(20,23)(22,26)(24,25));