Finite Group Databasebeta

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C₂×#72232166 #72325746

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

Aliases

Subgroups

At least 25510 conjugacy classes of subgroups; only the 38352 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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