Finite Group Databasebeta

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C2×C3×C5×D43⋊C3 #21440906

order7740
isoclinismisoclinic class of D43⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C5×D43⋊C3
unambiguous semidirect productD43⋊(C2×C32×C5)
unambiguous semidirect product(C43⋊C3)⋊(C22×C3×C5)
unambiguous semidirect product(C2×D43)⋊(C32×C5)
unambiguous semidirect product(C2×C43⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(C2×C3×D43)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D43)⋊C32
unambiguous semidirect product(C2×C3×C5×D43)⋊C3

Splittings

Fitting, socleC2×C3×C5×C43 ⋊ C2×C3
derived, SylowC43 ⋊ C22×C32×C5
HallC3×C5×C43⋊C3 ⋊ C22
HallC2×C5×D43 ⋊ C32
HallC3×C43⋊C3 ⋊ C22×C5
HallC5×C43 ⋊ C22×C32
HallC2×D43 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D43⋊C3
commutator, hypocenterC43C22×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C43C2×C3
LCSG ▷ C43
UCSC1 ◁ C2×C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7740, 74);