Finite Group Databasebeta

?

← Prev (#88391) Next (#88393) →

(C₂²⋊C₂₇)⋊C₄ #88392

• solvable
• monomial

Aliases

Splittings

Subgroups

45 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3,4)(5,6,8,7)(10,13)(11,17)(12,20)(14,15)(16,26)(18,19)(21,28)(22,27)(23,33)(24,32)(25,31)(29,30)(34,35);(6,7,8)(9,28,22,29,33,31,11,10,32,12,35,26,18,15,14,19,16,34,20,24,13,17,25,23,30,27,21)

Polycyclic presentation:

2^2,3^3,2^2|a^2=b,c^3=d^2e,d^3=e^2,c^a=c^2d,d^a=d^2e,e^a=e^2,f^a=g,g^a=f,f^c=g,g^c=fg

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 39);