Finite Group Databasebeta

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C7×C3⋊(C11⋊(D19⋊C3)) #39911885

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

Aliases

direct productC7×C3⋊(C11⋊(D19⋊C3))
unambiguous semidirect productC3⋊(C7×C11⋊(D19⋊C3))
unambiguous semidirect productC11⋊(C7×C3⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊(C7×D33)
unambiguous semidirect productD627⋊(C3×C7)

Splittings

Fitting, socleC3×C7×C11×C19 ⋊ C2×C3
derivedC3×C11×C19 ⋊ C2×C3×C7
HallC3×C7×C11×C19⋊C3 ⋊ C2
HallC3×C11×C19⋊C3 ⋊ C2×C7
HallC7×C11×C19 ⋊ C3×D3
HallC3×C7×C19⋊C3 ⋊ D11
HallC11×C19 ⋊ C3×D3×C7
HallC3×C19⋊C3 ⋊ C7×D11
HallC7×C19 ⋊ C3×D33
HallC7×C11 ⋊ C3⋊(D19⋊C3)
SylowC19 ⋊ C3×C7×D33
SylowC11 ⋊ C7×C3⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C11⋊(D19⋊C3))
commutator, cosocle, hypocenterC3×C11×C19C2×C3×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2×C3
LCSG ▷ C3×C11×C19
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4389

Conjugacy classes & character table

1071 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 112);