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D₂₄₅ #92436

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

Polycyclic presentation:

2,5,7^2|c^7=d^6,b^a=b^4,c^a=c^6d,d^a=d^6

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(490, 3);