Finite Group Databasebeta

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C₂×#72232112 #72298762

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

Aliases

Subgroups

At least 17278 conjugacy classes of subgroups; only the 42736 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

332 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((12,14)(15,16)(17,20)(18,19)(21,22), (4,6)(8,10)(11,12)(13,14)(16,19)(20,21), (3,4)(5,6)(7,8)(9,10)(15,16)(17,20)(18,19)(21,22), (4,6)(7,8,9,10)(16,19)(20,21), (4,6)(8,10)(15,17)(16,20)(18,22)(19,21), (3,4)(5,6)(7,8)(9,10)(15,16)(17,21)(18,19)(20,22), (1,2));