Finite Group Databasebeta

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C3×C4×C52×C37⋊C3 #45686121

order33300
automorphism?
homologyAbelianization (H1) = C32×C4×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C4×C52×C37⋊C3
unambiguous semidirect product(C4×C37)⋊(C32×C52)
unambiguous semidirect product(C3×C4×C37)⋊(C3×C52)
unambiguous semidirect product(C4×C5×C37)⋊(C32×C5)
unambiguous semidirect product(C3×C4×C5×C37)⋊(C3×C5)

Splittings

FittingC3×C4×C52×C37 ⋊ C3
derived, SylowC37 ⋊ C32×C4×C52
HallC4×C52×C37 ⋊ C32
HallC52×C37 ⋊ C32×C4
HallC4×C37 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC3×C4×C52C37⋊C3
commutator, hypocenterC37C32×C4×C52
FrattiniC2C2×C3×C52×C37⋊C3
FittingC3×C4×C52×C37C3
socleC2×C3×C52×C37C2×C3
prime radicalC2×C3×C52×C37⋊C3C2
cosocleC2×C37C2×C32×C52
LCSG ▷ C37
UCSC1 ◁ C3×C4×C52

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11100

Conjugacy classes & character table

4500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 394);