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C5×C13×D49⋊C3 #34062033

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×D49⋊C3
unambiguous semidirect productD49⋊(C3×C5×C13)
unambiguous semidirect product(C49⋊C3)⋊(C2×C5×C13)
unambiguous semidirect product(C5×D49)⋊(C3×C13)

Splittings

Fitting, HallC5×C13×C49 ⋊ C2×C3
derived, SylowC49 ⋊ C2×C3×C5×C13
HallC5×C13×C49⋊C3 ⋊ C2
HallC5×C13×D49 ⋊ C3
HallC13×C49⋊C3 ⋊ C2×C5
HallC13×D49 ⋊ C3×C5
HallC5×C49⋊C3 ⋊ C2×C13
HallC13×C49 ⋊ C2×C3×C5
HallC5×D49 ⋊ C3×C13
HallC5×C49 ⋊ C2×C3×C13
HallC49⋊C3 ⋊ C2×C5×C13
HallD49 ⋊ C3×C5×C13

Subgroups

subgroupG/H
center, hypercenterC5×C13D49⋊C3
commutator, cosocle, hypocenterC49C2×C3×C5×C13
FrattiniC7C5×C13×AGL(1,𝔽7)
FittingC5×C13×C49C2×C3
socleC5×C7×C13AGL(1,𝔽7)
LCSG ▷ C49
UCSC1 ◁ C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D13×D49⋊C3, D5×C13×D49⋊C3, D65×D49⋊C3, …
maximal normal subgroup ofC5×D13×D49⋊C3, D5×C13×D49⋊C3, D65×D49⋊C3, …
maximal quotient ofC5×C13×(C49⋊C3)⋊C4, C2×C5×C13×D49⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 26);