Finite Group Databasebeta

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C3×A4×C41⋊C5 #20301601

order7380
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C41⋊C5
unambiguous semidirect productC22⋊(C32×C41⋊C5)
unambiguous semidirect product(C22×C3)⋊(C3×C41⋊C5)
unambiguous semidirect productC41⋊(C3×C5×A4)
unambiguous semidirect product(C3×C41)⋊(C5×A4)
unambiguous semidirect product(A4×C41)⋊(C3×C5)
unambiguous semidirect product(C22×C41⋊C5)⋊C32
unambiguous semidirect product(C3×A4×C41)⋊C5
unambiguous semidirect product(C22×C3×C41⋊C5)⋊C3

Splittings

Fitting, socleC22×C3×C41 ⋊ C3×C5
derived, HallC22×C41 ⋊ C32×C5
HallC3×A4×C41 ⋊ C5
HallC22×C41⋊C5 ⋊ C32
SylowC41 ⋊ C3×C5×A4
SylowC22 ⋊ C32×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC3A4×C41⋊C5
commutator, hypocenterC22×C41C32×C5
FrattiniC1G
Fitting, socleC22×C3×C41C3×C5
LCSG ▷ C22×C41
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×A4×C41⋊C5, C3×A5×C41⋊C5
maximal normal subgroup ofC3×C5×A4×C41⋊C5
maximal quotient ofC3×A4×C41⋊C25, C3×C5×A4×C41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 79);