Finite Group Databasebeta

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C2×C5×C11×C3⋊D57 #49178787

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C11×C3⋊D57
unambiguous semidirect product(C2×C3)⋊(C5×C11×D57)
unambiguous semidirect product(C2×C19)⋊(C5×C11×C3⋊D3)

Splittings

Fitting, socleC2×C32×C5×C11×C19 ⋊ C2
derived, HallC32×C19 ⋊ C22×C5×C11
HallC32×C5×C11×C19 ⋊ C22
HallC32×C11×C19 ⋊ C22×C5
HallC5×C11×C19 ⋊ C2×C3⋊D3
HallC32×C5×C19 ⋊ C22×C11
HallC32×C5×C11 ⋊ C2×D19
HallC11×C19 ⋊ C2×C5×C3⋊D3
HallC32×C11 ⋊ C2×C5×D19
HallC5×C19 ⋊ C2×C11×C3⋊D3
HallC32×C5 ⋊ C2×C11×D19
SylowC19 ⋊ C2×C5×C11×C3⋊D3
SylowC32 ⋊ C2×C5×C11×D19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11C3⋊D57
commutator, cosocle, hypocenterC32×C19C22×C5×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C19C2
LCSG ▷ C32×C19
UCSC1 ◁ C2×C5×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18810

Conjugacy classes & character table

9570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 496);