Finite Group Databasebeta

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D₂₇₅ #10587750

• 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 36 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);(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(27,36)(28,35)(29,34)(30,33)(31,32)

Polycyclic presentation:

2,5,11,5|b^5=d^4,b^a=b^4d,c^a=c^10,d^a=d^4

Conjugacy classes & character table

139 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(550, 5);