Finite Group Databasebeta

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C13×D11×D19⋊C3 #45656712

order32604
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D11×D19⋊C3
unambiguous semidirect productD19⋊(C3×C13×D11)
unambiguous semidirect product(D11×D19)⋊(C3×C13)
unambiguous semidirect product(C11×D19⋊C3)⋊(C2×C13)
unambiguous semidirect product(D11×C19⋊C3)⋊(C2×C13)
unambiguous semidirect product(C11⋊(D19⋊C3))⋊(C2×C13)

Splittings

Fitting, socle, HallC11×C13×C19 ⋊ C22×C3
derived, HallC11×C19 ⋊ C22×C3×C13
HallC13×D11×D19 ⋊ C3
HallC11×C13×C19⋊C3 ⋊ C22
HallD11×D19 ⋊ C3×C13
HallC13×C19⋊C3 ⋊ C2×D11
HallC11×C19⋊C3 ⋊ C22×C13
HallC13×C19 ⋊ C2×C3×D11
HallC11×C13 ⋊ C2×D19⋊C3
HallC19⋊C3 ⋊ C2×C13×D11
SylowC19 ⋊ C2×C3×C13×D11
SylowC11 ⋊ C2×C13×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC13D11×D19⋊C3
commutator, cosocle, hypocenterC11×C19C22×C3×C13
FrattiniC1G
Fitting, socleC11×C13×C19C22×C3
LCSG ▷ C11×C19
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2717

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 62);