Finite Group Databasebeta

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C3×C5×A4×C43 #21440949

order7740
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C5×C43 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×A4×C43
unambiguous semidirect productC22⋊(C32×C5×C43)
unambiguous semidirect product(C22×C3)⋊(C3×C5×C43)
unambiguous semidirect product(C22×C5)⋊(C32×C43)
unambiguous semidirect product(C22×C3×C5)⋊(C3×C43)

Splittings

Fitting, socleC22×C3×C5×C43 ⋊ C3
derived, SylowC22 ⋊ C32×C5×C43
HallC22×C5×C43 ⋊ C32
HallC22×C43 ⋊ C32×C5
HallC22×C5 ⋊ C32×C43

Subgroups

subgroupG/H
center, hypercenterC3×C5×C43A4
commutator, hypocenterC22C32×C5×C43
FrattiniC1G
Fitting, socleC22×C3×C5×C43C3
LCSG ▷ C22
UCSC1 ◁ C3×C5×C43

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7740, 117);