Finite Group Databasebeta

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C3×A4×C101⋊C5 #32911446

order18180
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C101⋊C5
unambiguous semidirect productC22⋊(C32×C101⋊C5)
unambiguous semidirect product(C22×C3)⋊(C3×C101⋊C5)
unambiguous semidirect productC101⋊(C3×C5×A4)
unambiguous semidirect product(C3×C101)⋊(C5×A4)
unambiguous semidirect product(A4×C101)⋊(C3×C5)
unambiguous semidirect product(C22×C101⋊C5)⋊C32
unambiguous semidirect product(C3×A4×C101)⋊C5
unambiguous semidirect product(C22×C3×C101⋊C5)⋊C3

Splittings

Fitting, socleC22×C3×C101 ⋊ C3×C5
derived, HallC22×C101 ⋊ C32×C5
HallC3×A4×C101 ⋊ C5
HallC22×C101⋊C5 ⋊ C32
SylowC101 ⋊ C3×C5×A4
SylowC22 ⋊ C32×C101⋊C5

Subgroups

subgroupG/H
center, hypercenterC3A4×C101⋊C5
commutator, cosocle, hypocenterC22×C101C32×C5
FrattiniC1G
Fitting, socleC22×C3×C101C3×C5
LCSG ▷ C22×C101
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1212

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 79);