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C₃×#63045 #10681652

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

7484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 27 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 56033);