Finite Group Databasebeta

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C3×C5×C11⋊((C19⋊C3)⋊C4) #49178463

order37620
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C11⋊((C19⋊C3)⋊C4)
unambiguous semidirect product(C19⋊C3)⋊(C3×C5×Dic11)
unambiguous semidirect product(C5×Dic209)⋊C32
unambiguous semidirect product(C3×C5×Dic209)⋊C3

Splittings

derived, HallC11×C19 ⋊ C32×C4×C5
HallC3×C5×C11×C19⋊C3 ⋊ C4
HallC5×Dic209 ⋊ C32
HallC3×C11×C19⋊C3 ⋊ C4×C5
HallC5×C11×C19 ⋊ C32×C4
HallC3×C5×C19⋊C3 ⋊ Dic11
HallDic209 ⋊ C32×C5
HallC3×C19⋊C3 ⋊ C5×Dic11
HallC5×C19 ⋊ C32×Dic11
HallC5×C11 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C32×C5×Dic11
SylowC11 ⋊ C3×C5×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C11⋊(D19⋊C3)
commutator, hypocenterC11×C19C32×C4×C5
FrattiniC2C3×C5×C11⋊(D19⋊C3)
Fitting, socleC2×C3×C5×C11×C19C2×C3
prime radicalC2×C3×C5×C11×C19⋊C3C2
cosocleC2×C11×C19C2×C32×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C3×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12540

Conjugacy classes & character table

1620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 172);