Finite Group Databasebeta

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C₂×#72232350 #72338077

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

Aliases

Subgroups

At least 10640 conjugacy classes of subgroups; only the 33416 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 30 points:

(3,4,5,6)(8,11)(9,13)(15,16)(17,21)(18,20)(19,22)(24,27)(25,29);(7,8)(9,12)(10,11)(13,14)(15,16,18,20)(17,19,22,21);(4,6)(8,11)(9,13)(17,22)(19,21)(23,24,26,27)(25,30,29,28);(3,4)(5,6)(9,13)(12,14);(1,2);(7,8)(9,12)(10,11)(13,14)(15,17)(16,19)(18,22)(20,21)(23,24)(25,28)(26,27)(29,30);(7,9)(8,12)(10,13)(11,14)(15,16)(17,21)(18,20)(19,22)(23,25,26,29)(24,28,27,30)

Conjugacy classes & character table

296 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((3,4,5,6)(8,11)(9,13)(15,16)(17,21)(18,20)(19,22)(24,27)(25,29), (7,8)(9,12)(10,11)(13,14)(15,16,18,20)(17,19,22,21), (4,6)(8,11)(9,13)(17,22)(19,21)(23,24,26,27)(25,30,29,28), (3,4)(5,6)(9,13)(12,14), (1,2), (7,8)(9,12)(10,11)(13,14)(15,17)(16,19)(18,22)(20,21)(23,24)(25,28)(26,27)(29,30), (7,9)(8,12)(10,13)(11,14)(15,16)(17,21)(18,20)(19,22)(23,25,26,29)(24,28,27,30));