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C13×C5⋊(D49⋊C3) #34062049

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C5⋊(D49⋊C3)
unambiguous semidirect productC5⋊(C13×D49⋊C3)
unambiguous semidirect product(C49⋊C3)⋊(D5×C13)
unambiguous semidirect productD245⋊(C3×C13)

Splittings

Fitting, HallC5×C13×C49 ⋊ C2×C3
derived, HallC5×C49 ⋊ C2×C3×C13
HallC5×C13×C49⋊C3 ⋊ C2
HallC13×D245 ⋊ C3
HallC13×C49⋊C3 ⋊ D5
HallC5×C49⋊C3 ⋊ C2×C13
HallC13×C49 ⋊ C3×D5
HallD245 ⋊ C3×C13
HallC49⋊C3 ⋊ D5×C13
HallC5×C13 ⋊ D49⋊C3
SylowC49 ⋊ C3×D5×C13
SylowC5 ⋊ C13×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC13C5⋊(D49⋊C3)
commutator, cosocle, hypocenterC5×C49C2×C3×C13
FrattiniC7C13×C5⋊AGL(1,𝔽7)
FittingC5×C13×C49C2×C3
socleC5×C7×C13AGL(1,𝔽7)
LCSG ▷ C5×C49
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD13×C5⋊(D49⋊C3), D5×C13×D49⋊C3, (C5⋊(D49⋊C3))⋊D13, …
maximal normal subgroup ofD13×C5⋊(D49⋊C3), D5×C13×D49⋊C3, (C5⋊(D49⋊C3))⋊D13, …
maximal quotient ofC13×(C49⋊C3)⋊Dic5, C2×C13×C5⋊(D49⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 42);