Finite Group Databasebeta

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C₂×#120×#392 #72320525

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

Aliases

Subgroups

At least 6700 conjugacy classes of subgroups; only the 94363 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

616 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((11,12)(13,14)(15,16,18,17)(19,20,22,21), (4,6)(8,10)(12,14)(16,17)(19,20,22,21), (16,17)(20,21), (1,2), (8,10), (4,6)(8,10), (3,4)(5,6)(7,8,9,10)(11,12)(13,14)(15,17,18,16)(19,21,22,20));