Finite Group Databasebeta

← Prev (#34087140) Next (#34087142) →

C5×A4×C109⋊C3 #34087141

order19620
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×A4×C109⋊C3
unambiguous semidirect product(C22×C109⋊C3)⋊(C3×C5)
unambiguous semidirect product(A4×C109)⋊(C3×C5)
unambiguous semidirect product(C22⋊(C109⋊C3))⋊(C3×C5)
unambiguous semidirect product(C22×C5×C109⋊C3)⋊C3
unambiguous semidirect product(C5×A4×C109)⋊C3
unambiguous semidirect product(C5×C22⋊(C109⋊C3))⋊C3

Splittings

Fitting, socle, HallC22×C5×C109 ⋊ C32
derived, HallC22×C109 ⋊ C32×C5
HallC5×C109 ⋊ C3×A4
SylowC109 ⋊ C3×C5×A4
HallC22×C5 ⋊ C3×C109⋊C3
SylowC22 ⋊ C3×C5×C109⋊C3

Subgroups

subgroupG/H
center, hypercenterC5A4×C109⋊C3
commutator, cosocle, hypocenterC22×C109C32×C5
FrattiniC1G
Fitting, socleC22×C5×C109C32
LCSG ▷ C22×C109
UCSC1 ◁ C5

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2180

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19620, 109);