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C₂²×C₇₃⋊C₃ #11724822

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 77 points:

(1,2)(6,7,9)(8,11,16)(10,14,13)(12,18,26)(15,21,23)(17,24,20)(19,28,39)(22,31,36)(25,34,33)(27,37,30)(29,41,54)(32,44,51)(35,42,48)(38,49,46)(40,52,43)(45,57,66)(47,58,63)(50,62,61)(53,64,59)(55,67,56)(60,70,73)(65,72,71)(68,74,69)(75,77,76);(3,4)(5,6,8,12,19,29,42,21,7,10,15,22,32,45,58,31,11,17,25,35,47,60,70,44,18,27,38,50,54,66,73,57,28,40,53,65,67,39,51,63,41,55,68,75,74,52,26,36,48,61,71,76,77,64,37,16,23,33,46,59,69,72,49,24,9,13,20,30,43,56,62,34,14)

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(876, 12);