Finite Group Databasebeta

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C₂×#7940447 #72304498

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

Aliases

Subgroups

At least 6154 conjugacy classes of subgroups; only the 31893 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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