Finite Group Databasebeta

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C3×C5×C5⋊(D73⋊C3) #45659488

order32850
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C5⋊(D73⋊C3)
unambiguous semidirect productC5⋊(C3×C5×D73⋊C3)
unambiguous semidirect product(C73⋊C3)⋊(C3×C5×D5)
unambiguous semidirect productD365⋊(C32×C5)
unambiguous semidirect product(C3×D365)⋊(C3×C5)
unambiguous semidirect product(C5×D365)⋊C32
unambiguous semidirect product(C3×C5×D365)⋊C3

Splittings

Fitting, socleC3×C52×C73 ⋊ C2×C3
derivedC5×C73 ⋊ C2×C32×C5
HallC3×C52×C73⋊C3 ⋊ C2
HallC5×D365 ⋊ C32
HallC52×C73 ⋊ C2×C32
HallC3×C73⋊C3 ⋊ C5×D5
SylowC73 ⋊ C32×C5×D5
SylowC52 ⋊ C3×D73⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5C5⋊(D73⋊C3)
commutator, cosocle, hypocenterC5×C73C2×C32×C5
FrattiniC1G
Fitting, socleC3×C52×C73C2×C3
LCSG ▷ C5×C73
UCSC1 ◁ C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2190

Conjugacy classes & character table

1080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32850, 91);