Finite Group Databasebeta

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C11×D39⋊D19 #45656790

order32604
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D39⋊D19
unambiguous semidirect productD39⋊(C11×D19)
unambiguous semidirect productD57⋊(C11×D13)
unambiguous semidirect productD247⋊(D3×C11)

Splittings

Fitting, socle, HallC3×C11×C13×C19 ⋊ C22
derived, HallC3×C13×C19 ⋊ C22×C11
HallC11×C13×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C2×D13
HallC3×C11×C13 ⋊ C2×D19
HallC13×C19 ⋊ C2×D3×C11
HallC11×C19 ⋊ D3×D13
HallC11×C13 ⋊ D3×D19
HallC3×C19 ⋊ C2×C11×D13
HallC3×C13 ⋊ C2×C11×D19
HallC3×C11 ⋊ D13×D19
SylowC19 ⋊ D3×C11×D13
SylowC13 ⋊ D3×C11×D19
SylowC3 ⋊ C11×D13×D19

Subgroups

subgroupG/H
center, hypercenterC11D39⋊D19
commutator, cosocle, hypocenterC3×C13×C19C22×C11
FrattiniC1G
Fitting, socleC3×C11×C13×C19C22
LCSG ▷ C3×C13×C19
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8151

Conjugacy classes & character table

2343 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 140);