Finite Group Databasebeta

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C₂×#12547 #492841

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

Aliases

Subgroups

1698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,11,16,12,18,26,35,13,17,27,34,10,15,24,32)(9,19,22,36,23,14,28,30,20,31,25,38,21,29,37,33);(4,6)(7,9)(8,14,17,29)(10,21)(11,25)(12,23)(13,20)(15,19,18,31)(16,33,34,30)(22,27)(24,28)(26,37)(32,38,35,36);(9,20)(14,29)(19,31)(21,23)(22,25)(28,37)(30,33)(36,38)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400037);