Finite Group Databasebeta

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C3×C5×C17×C37⋊C3 #43246700

order28305
automorphism?
homologyAbelianization (H1) = C32×C5×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C17×C37⋊C3
unambiguous semidirect productC37⋊(C32×C5×C17)
unambiguous semidirect product(C3×C37)⋊(C3×C5×C17)
unambiguous semidirect product(C5×C37)⋊(C32×C17)
unambiguous semidirect product(C3×C5×C37)⋊(C3×C17)
unambiguous semidirect product(C17×C37)⋊(C32×C5)
unambiguous semidirect product(C3×C17×C37)⋊(C3×C5)
unambiguous semidirect product(C5×C17×C37)⋊C32
unambiguous semidirect product(C3×C5×C17×C37)⋊C3

Splittings

Fitting, socleC3×C5×C17×C37 ⋊ C3
derived, SylowC37 ⋊ C32×C5×C17
HallC5×C17×C37 ⋊ C32
HallC17×C37 ⋊ C32×C5
HallC5×C37 ⋊ C32×C17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C17C37⋊C3
commutator, cosocle, hypocenterC37C32×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C37C3
LCSG ▷ C37
UCSC1 ◁ C3×C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9435

Conjugacy classes & character table

3825 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28305, 5);