Finite Group Databasebeta

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C2×C3×C5×C7×C19⋊C3 #26046216

order11970
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×C7×C19⋊C3
unambiguous semidirect product(C2×C19)⋊(C32×C5×C7)
unambiguous semidirect product(C2×C3×C19)⋊(C3×C5×C7)
unambiguous semidirect product(C2×C5×C19)⋊(C32×C7)
unambiguous semidirect product(C2×C3×C5×C19)⋊(C3×C7)

Splittings

Fitting, socleC2×C3×C5×C7×C19 ⋊ C3
derived, SylowC19 ⋊ C2×C32×C5×C7
HallC2×C5×C7×C19 ⋊ C32
HallC5×C7×C19 ⋊ C2×C32
HallC2×C7×C19 ⋊ C32×C5
HallC2×C5×C19 ⋊ C32×C7
HallC7×C19 ⋊ C2×C32×C5
HallC5×C19 ⋊ C2×C32×C7
HallC2×C19 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7C19⋊C3
commutator, cosocle, hypocenterC19C2×C32×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C19C3
LCSG ▷ C19
UCSC1 ◁ C2×C3×C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1890 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C7×(C19⋊C3)⋊C4, C3×C5×(C19⋊C3)⋊Dic7, C3×C5×Dic7×C19⋊C3, …
maximal normal subgroup ofC3×C5×C7×(C19⋊C3)⋊C4, C3×C5×(C19⋊C3)⋊Dic7, C3×C5×Dic7×C19⋊C3, …
maximal quotient ofC3×C4×C5×C7×C19⋊C3, C22×C3×C5×C7×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 145);