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C13×C11⋊(D19⋊C3) #30654451

order16302
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C11⋊(D19⋊C3)
unambiguous semidirect productC11⋊(C13×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C13×D11)
unambiguous semidirect productD209⋊(C3×C13)

Splittings

Fitting, socle, HallC11×C13×C19 ⋊ C2×C3
derived, HallC11×C19 ⋊ C2×C3×C13
HallC11×C13×C19⋊C3 ⋊ C2
HallC13×D209 ⋊ C3
HallC13×C19⋊C3 ⋊ D11
HallC11×C19⋊C3 ⋊ C2×C13
HallD209 ⋊ C3×C13
HallC13×C19 ⋊ C3×D11
HallC11×C13 ⋊ D19⋊C3
HallC19⋊C3 ⋊ C13×D11
SylowC19 ⋊ C3×C13×D11
SylowC11 ⋊ C13×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC13C11⋊(D19⋊C3)
commutator, cosocle, hypocenterC11×C19C2×C3×C13
FrattiniC1G
Fitting, socleC11×C13×C19C2×C3
LCSG ▷ C11×C19
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2717

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC13×D11×D19⋊C3, D13×C11⋊(D19⋊C3), (C11⋊(D19⋊C3))⋊D13, …
maximal normal subgroup ofC13×D11×D19⋊C3, D13×C11⋊(D19⋊C3), (C11⋊(D19⋊C3))⋊D13, …
maximal quotient ofC13×C11⋊((C19⋊C3)⋊C4), C2×C13×C11⋊(D19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16302, 37);