Finite Group Databasebeta

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C11×D19×D13⋊C3 #45656708

order32604
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D19×D13⋊C3
unambiguous semidirect productD13⋊(C3×C11×D19)
unambiguous semidirect product(D19×C13⋊C3)⋊(C2×C11)
unambiguous semidirect product(C19×D13⋊C3)⋊(C2×C11)
unambiguous semidirect product((C13⋊C3)⋊D19)⋊(C2×C11)

Splittings

Fitting, socle, HallC11×C13×C19 ⋊ C22×C3
derived, HallC13×C19 ⋊ C22×C3×C11
HallC11×D13×D19 ⋊ C3
HallC11×C19×C13⋊C3 ⋊ C22
HallD13×D19 ⋊ C3×C11
HallC19×C13⋊C3 ⋊ C22×C11
HallC11×C13⋊C3 ⋊ C2×D19
HallC11×C19 ⋊ C2×D13⋊C3
HallC11×C13 ⋊ C2×C3×D19
HallC13⋊C3 ⋊ C2×C11×D19
SylowC19 ⋊ C2×C11×D13⋊C3
SylowC13 ⋊ C2×C3×C11×D19

Subgroups

subgroupG/H
center, hypercenterC11D19×D13⋊C3
commutator, cosocle, hypocenterC13×C19C22×C3×C11
FrattiniC1G
Fitting, socleC11×C13×C19C22×C3
LCSG ▷ C13×C19
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2717

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 58);