Finite Group Databasebeta

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C32×C4×C19×C11⋊C5 #49178477

order37620
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C19 · Schur multiplier (H2) = C3

Aliases

direct productC32×C4×C19×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C32×C5×C19)
unambiguous semidirect product(C3×C4×C11)⋊(C3×C5×C19)
unambiguous semidirect product(C32×C4×C11)⋊(C5×C19)
unambiguous semidirect product(C32×C4×C11×C19)⋊C5

Splittings

Fitting, HallC32×C4×C11×C19 ⋊ C5
derived, SylowC11 ⋊ C32×C4×C5×C19
HallC32×C11×C19 ⋊ C4×C5
HallC4×C11×C19 ⋊ C32×C5
HallC32×C4×C11 ⋊ C5×C19
HallC11×C19 ⋊ C32×C4×C5
HallC32×C11 ⋊ C4×C5×C19
HallC4×C11 ⋊ C32×C5×C19

Subgroups

subgroupG/H
center, hypercenterC32×C4×C19C11⋊C5
commutator, hypocenterC11C32×C4×C5×C19
FrattiniC2C2×C32×C19×C11⋊C5
FittingC32×C4×C11×C19C5
socleC2×C32×C11×C19C2×C5
prime radicalC2×C32×C19×C11⋊C5C2
cosocleC2×C11C2×C32×C5×C19
LCSG ▷ C11
UCSC1 ◁ C32×C4×C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7524

Conjugacy classes & character table

4788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 186);