Finite Group Databasebeta

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C₂×#72337224 #72339962

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

Aliases

Subgroups

At least 6844 conjugacy classes of subgroups; only the 40160 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

320 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((8,10)(12,16)(14,17), (11,12,15,16)(13,17,18,14), (4,6)(8,10)(19,20,22,23)(21,24,26,25), (4,6)(20,23)(24,25), (1,2)(11,13)(12,17)(14,16)(15,18)(19,21)(20,24)(22,26)(23,25), (11,13)(12,17)(14,16)(15,18)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(7,8)(9,10)(11,14,15,17)(12,18,16,13)(19,20)(21,25)(22,23)(24,26));