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C19×C3⋊(C3⋊(Dic11⋊C5)) #49178457

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

Aliases

direct productC19×C3⋊(C3⋊(Dic11⋊C5))
unambiguous semidirect productC3⋊(C19×C3⋊(Dic11⋊C5))
unambiguous semidirect product(C11⋊C5)⋊(C19×C3⋊Dic3)
unambiguous semidirect product(C3⋊Dic33)⋊(C5×C19)
unambiguous semidirect product(C19×C3⋊Dic33)⋊C5

Splittings

derived, HallC32×C11 ⋊ C4×C5×C19
HallC32×C19×C11⋊C5 ⋊ C4
HallC19×C3⋊Dic33 ⋊ C5
HallC32×C11×C19 ⋊ C4×C5
HallC19×C11⋊C5 ⋊ C3⋊Dic3
HallC32×C11⋊C5 ⋊ C4×C19
HallC3⋊Dic33 ⋊ C5×C19
HallC11×C19 ⋊ C5×C3⋊Dic3
HallC32×C19 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C19×C3⋊Dic3
SylowC11 ⋊ C5×C19×C3⋊Dic3
SylowC32 ⋊ C19×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C19C3⋊(C3⋊AGL(1,𝔽11))
commutator, hypocenterC32×C11C4×C5×C19
FrattiniC2C19×C3⋊(C3⋊AGL(1,𝔽11))
Fitting, socleC2×C32×C11×C19C2×C5
prime radicalC2×C32×C19×C11⋊C5C2
cosocleC2×C32×C11C2×C5×C19
LCSG ▷ C32×C11
UCSC1 ◁ C2×C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7524

Conjugacy classes & character table

1482 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 166);