Finite Group Databasebeta

← Prev (#13108181) Next (#13108183) →

#13108182

order1620
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

Fitting, HallC5×AΣL(1,𝔽27) ⋊ C4
derivedC5×H(3,𝔽3) ⋊ C3×C4
SylowAΣL(1,𝔽27) ⋊ AGL(1,𝔽5)
SylowC5 ⋊ #66321

Subgroups

subgroupG/H
center, hypercenterC3(C3⋊ΓL(1,𝔽16))⋊C3
commutator, hypocenterC5×H(3,𝔽3)C3×C4
FrattiniC32C3×ΓL(1,𝔽16)
FittingC5×AΣL(1,𝔽27)C4
socleC3×C5(C3⋊Dic3)⋊C3
prime radicalD5×AΣL(1,𝔽27)C2
cosocleD5×H(3,𝔽3)C2×C3
LCSG ▷ C5×H(3,𝔽3)
UCSC1 ◁ C3

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 45

Polycyclic presentation:

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

Conjugacy classes & character table

61 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 88);