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Dic₂₂₅ #11744591

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

27 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 38 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

Polycyclic presentation:

2^2,3,5,3,5|a^2=b,c^3=e,d^5=f,c^a=c^2e^2,d^a=d^4f^4,e^a=e^2,f^a=f^4

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(900, 3);