Finite Group Databasebeta

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C3×C11×(C19⋊C3)⋊D7 #39911879

order26334
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×(C19⋊C3)⋊D7
unambiguous semidirect product(C19⋊C3)⋊(C3×C11×D7)

Splittings

Fitting, socleC3×C7×C11×C19 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C32×C11
HallC3×C7×C11×C19⋊C3 ⋊ C2
HallC11×D133 ⋊ C32
HallC3×C11×C19⋊C3 ⋊ D7
HallC7×C11×C19 ⋊ C2×C32
HallC3×C7×C19⋊C3 ⋊ C2×C11
HallD133 ⋊ C32×C11
HallC11×C19 ⋊ C32×D7
HallC3×C19⋊C3 ⋊ C11×D7
HallC7×C11 ⋊ C3×D19⋊C3
SylowC19 ⋊ C32×C11×D7
SylowC7 ⋊ C3×C11×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C11(C19⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C19C2×C32×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C3×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4389

Conjugacy classes & character table

1188 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 106);