Finite Group Databasebeta

← Prev (#44477484) Next (#44477486) →

C3×C5×#10621721⋊C3 #44477485

order30420
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×#10621721⋊C3
unambiguous semidirect product#10621721⋊(C32×C5)
unambiguous semidirect product(C3×#10621721)⋊(C3×C5)
unambiguous semidirect product(C5×#10621721)⋊C32
unambiguous semidirect product(C3×C5×#10621721)⋊C3

Splittings

FittingC3×C5×C169 ⋊ C3×C4
derived, SylowC169 ⋊ C32×C4×C5
HallC3×C5×C169⋊C3 ⋊ C4
HallC5×#10621721 ⋊ C32
HallC3×C169⋊C3 ⋊ C4×C5
HallC5×C169 ⋊ C32×C4
Hall#10621721 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5#10621721⋊C3
commutator, hypocenterC169C32×C4×C5
FrattiniC13C3×C5×AGL(1,𝔽13)
FittingC3×C5×C169C3×C4
socleC3×C5×C13AGL(1,𝔽13)
prime radicalC3×C5×D169⋊C3C2
cosocleD169C2×C32×C5
LCSG ▷ C169
UCSC1 ◁ C3×C5

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2535

Conjugacy classes & character table

390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 74);