Finite Group Databasebeta

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C₂×#7675477 #72240940

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

Aliases

Subgroups

110377 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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