Finite Group Databasebeta

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C3×C5×(C151⋊C3)⋊C5 #46800852

order33975
automorphism?
homologyAbelianization (H1) = C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C5×(C151⋊C3)⋊C5
unambiguous semidirect product(C151⋊C3)⋊(C3×C52)
unambiguous semidirect product(C151⋊C5)⋊(C32×C5)
unambiguous semidirect product(C3×C151⋊C3)⋊C52
unambiguous semidirect product(C3×C151⋊C5)⋊(C3×C5)
unambiguous semidirect product(C5×C151⋊C3)⋊(C3×C5)
unambiguous semidirect product(C5×C151⋊C5)⋊C32
unambiguous semidirect product(C3×C5×C151⋊C3)⋊C5
unambiguous semidirect product(C3×C5×C151⋊C5)⋊C3

Splittings

Fitting, socleC3×C5×C151 ⋊ C3×C5
derived, SylowC151 ⋊ C32×C52
HallC5×C151⋊C5 ⋊ C32
HallC3×C151⋊C3 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC3×C5(C151⋊C3)⋊C5
commutator, cosocle, hypocenterC151C32×C52
FrattiniC1G
Fitting, socleC3×C5×C151C3×C5
LCSG ▷ C151
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2265

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33975, 20);