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C19×C11⋊#4380 #49178651

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

Aliases

direct productC19×C11⋊#4380
unambiguous semidirect productC11⋊(C19×#4380)

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C4
derived, HallC32×C5×C11 ⋊ C4×C19
HallC32×C11×C19 ⋊ AGL(1,𝔽5)
HallC5×C11×C19 ⋊ #157
HallC32×C5×C19 ⋊ Dic11
HallC11×C19 ⋊ #4380
HallC32×C19 ⋊ C11⋊AGL(1,𝔽5)
HallC32×C11 ⋊ C19×AGL(1,𝔽5)
HallC5×C19 ⋊ C11⋊#157
HallC5×C11 ⋊ C19×#157
HallC32×C5 ⋊ C19×Dic11
SylowC11 ⋊ C19×#4380
SylowC32 ⋊ C19×C11⋊AGL(1,𝔽5)
SylowC5 ⋊ C19×C11⋊#157

Subgroups

subgroupG/H
center, hypercenterC19C11⋊#4380
commutator, hypocenterC32×C5×C11C4×C19
FrattiniC1G
Fitting, socleC32×C5×C11×C19C4
prime radicalC11×C19×C3⋊D15C2
cosocleC11×C3⋊D15C2×C19
LCSG ▷ C32×C5×C11
UCSC1 ◁ C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Conjugacy classes & character table

2565 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 360);