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D₆₃₇ #11929699

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem
• Frobenius
• ambivalent

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 62 points:

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

Polycyclic presentation:

2,7,13,7|b^7=d^6,b^a=b^6d,c^a=c^12,d^a=d^6

Conjugacy classes & character table

320 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1274, 3);