Finite Group Databasebeta

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C2×C32×D5×C11×C19 #49178774

order37620
automorphism?
homologyAbelianization (H1) = C22×C32×C11×C19 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×D5×C11×C19
unambiguous semidirect productC5⋊(C22×C32×C11×C19)
unambiguous semidirect product(C2×C5)⋊(C2×C32×C11×C19)

Splittings

Fitting, socleC2×C32×C5×C11×C19 ⋊ C2
derived, SylowC5 ⋊ C22×C32×C11×C19
HallC32×C5×C11×C19 ⋊ C22
HallC5×C11×C19 ⋊ C22×C32
HallC32×C5×C19 ⋊ C22×C11
HallC32×C5×C11 ⋊ C22×C19
HallC5×C19 ⋊ C22×C32×C11
HallC5×C11 ⋊ C22×C32×C19
HallC32×C5 ⋊ C22×C11×C19

Subgroups

subgroupG/H
center, hypercenterC2×C32×C11×C19D5
commutator, cosocle, hypocenterC5C22×C32×C11×C19
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C19C2
LCSG ▷ C5
UCSC1 ◁ C2×C32×C11×C19

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18810

Conjugacy classes & character table

15048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 483);