Finite Group Databasebeta

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C22×C3×C11⋊C5×C19⋊C3 #49178571

order37620
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×C11⋊C5×C19⋊C3
unambiguous semidirect product(C22×C3×C11×C19⋊C3)⋊C5

Splittings

Fitting, socleC22×C3×C11×C19 ⋊ C3×C5
derived, HallC11×C19 ⋊ C22×C32×C5
HallC22×C3×C11×C19⋊C3 ⋊ C5
HallC22×C19×C11⋊C5 ⋊ C32
HallC3×C11×C19⋊C3 ⋊ C22×C5
HallC19×C11⋊C5 ⋊ C22×C32
HallC22×C11×C19 ⋊ C32×C5
HallC22×C19 ⋊ C32×C11⋊C5
HallC22×C11 ⋊ C3×C5×C19⋊C3
SylowC19 ⋊ C22×C32×C11⋊C5
SylowC11 ⋊ C22×C3×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC22×C3C11⋊C5×C19⋊C3
commutator, cosocle, hypocenterC11×C19C22×C32×C5
FrattiniC1G
Fitting, socleC22×C3×C11×C19C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C22×C3

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2508

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 280);