Finite Group Databasebeta

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C₂×#7940293 #72304459

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

Aliases

Subgroups

At least 6100 conjugacy classes of subgroups; only the 31853 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

190 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((1,2)(4,6)(8,11)(9,13)(15,16,22,27)(17,23,26,21)(18,20,25,30)(19,24,29,28), (4,6)(7,8,10,11)(9,12,13,14)(15,17,22,26)(16,21,27,23)(18,24,25,28)(19,30,29,20), (7,8)(9,12)(10,11)(13,14)(15,17)(16,23)(18,28)(19,20)(21,27)(22,26)(24,25)(29,30), (4,6)(7,8,10,11)(9,12,13,14)(15,18,22,25)(16,20,27,30)(17,28,26,24)(19,21,29,23), (3,4,5,6)(8,11)(12,14)(15,19)(16,24)(17,20)(18,21)(22,29)(23,25)(26,30)(27,28), (7,8)(9,14)(10,11)(12,13)(15,20)(16,25)(17,19)(18,27)(21,28)(22,30)(23,24)(26,29), (7,9,10,13)(8,12,11,14)(15,21)(16,26)(17,27)(18,29)(19,25)(20,24)(22,23)(28,30));