Finite Group Databasebeta

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C₂×#72219261 #72325654

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

Aliases

Subgroups

At least 14470 conjugacy classes of subgroups; only the 42368 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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