Finite Group Databasebeta

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C2×C3×C52×D37⋊C3 #45686338

order33300
automorphism?
homologyAbelianization (H1) = C22×C32×C52 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C3×C52×D37⋊C3
unambiguous semidirect productD37⋊(C2×C32×C52)
unambiguous semidirect product(C37⋊C3)⋊(C22×C3×C52)
unambiguous semidirect product(C2×D37)⋊(C32×C52)
unambiguous semidirect product(C2×C37⋊C3)⋊(C2×C3×C52)
unambiguous semidirect product(C2×C3×D37)⋊(C3×C52)
unambiguous semidirect product(C2×C5×D37)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C5×D37)⋊(C3×C5)

Splittings

Fitting, socleC2×C3×C52×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C22×C32×C52
HallC3×C52×C37⋊C3 ⋊ C22
HallC2×C52×D37 ⋊ C32
HallC52×C37 ⋊ C22×C32
HallC3×C37⋊C3 ⋊ C22×C52
HallC2×D37 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C52D37⋊C3
commutator, cosocle, hypocenterC37C22×C32×C52
FrattiniC1G
Fitting, socleC2×C3×C52×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C2×C3×C52

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5550

Conjugacy classes & character table

1800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 611);