Finite Group Databasebeta

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C₂×#12780 #493619

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

Aliases

Subgroups

2419 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400815);