Finite Group Databasebeta

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C3×C5×C112×A4 #36345372

order21780
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C5×C112 · Schur multiplier (H2) = C2×C3×C11

Aliases

direct productC3×C5×C112×A4
unambiguous semidirect productC22⋊(C32×C5×C112)
unambiguous semidirect product(C22×C3)⋊(C3×C5×C112)
unambiguous semidirect product(C22×C5)⋊(C32×C112)
unambiguous semidirect product(C22×C3×C5)⋊(C3×C112)
unambiguous semidirect product(C22×C5×C11)⋊(C32×C11)
unambiguous semidirect product(C22×C3×C5×C11)⋊(C3×C11)

Splittings

Fitting, socleC22×C3×C5×C112 ⋊ C3
derived, SylowC22 ⋊ C32×C5×C112
HallC22×C5×C112 ⋊ C32
HallC22×C112 ⋊ C32×C5
HallC22×C5 ⋊ C32×C112

Subgroups

subgroupG/H
center, hypercenterC3×C5×C112A4
commutator, cosocle, hypocenterC22C32×C5×C112
FrattiniC1G
Fitting, socleC22×C3×C5×C112C3
LCSG ▷ C22
UCSC1 ◁ C3×C5×C112

392 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 721);