Finite Group Databasebeta

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C7×C11×C3⋊(D19⋊C3) #39911883

order26334
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×C3⋊(D19⋊C3)
unambiguous semidirect productC3⋊(C7×C11×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(D3×C7×C11)
unambiguous semidirect productD57⋊(C3×C7×C11)
unambiguous semidirect product(C11×D57)⋊(C3×C7)

Splittings

Fitting, socleC3×C7×C11×C19 ⋊ C2×C3
derivedC3×C19 ⋊ C2×C3×C7×C11
HallC3×C7×C11×C19⋊C3 ⋊ C2
HallC3×C11×C19⋊C3 ⋊ C2×C7
HallC7×C11×C19 ⋊ C3×D3
HallC3×C7×C19⋊C3 ⋊ C2×C11
HallC11×C19 ⋊ C3×D3×C7
HallC3×C19⋊C3 ⋊ C2×C7×C11
HallC7×C19 ⋊ C3×D3×C11
SylowC19 ⋊ C3×D3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC7×C11C3⋊(D19⋊C3)
commutator, cosocle, hypocenterC3×C19C2×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2×C3
LCSG ▷ C3×C19
UCSC1 ◁ C7×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4389

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 110);