Finite Group Databasebeta

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D5×C13⋊C3×C49 #34062040

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1

Aliases

direct productD5×C13⋊C3×C49
unambiguous semidirect productC5⋊(C2×C13⋊C3×C49)
unambiguous semidirect product(D5×C13)⋊(C3×C49)

Splittings

Fitting, HallC5×C13×C49 ⋊ C2×C3
derived, HallC5×C13 ⋊ C2×C3×C49
HallC5×C13⋊C3×C49 ⋊ C2
HallD5×C13×C49 ⋊ C3
HallC13×C49 ⋊ C3×D5
HallC5×C49 ⋊ C2×C13⋊C3
HallC5×C13⋊C3 ⋊ C2×C49
HallD5×C13 ⋊ C3×C49
SylowC13 ⋊ C3×D5×C49
SylowC5 ⋊ C2×C13⋊C3×C49

Subgroups

subgroupG/H
center, hypercenterC49D5×C13⋊C3
commutator, hypocenterC5×C13C2×C3×C49
FrattiniC7C7×D5×C13⋊C3
FittingC5×C13×C49C2×C3
socle, cosocleC5×C7×C13C2×C3×C7
prime radicalC7×D5×C13⋊C3C7
LCSG ▷ C5×C13
UCSC1 ◁ C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC49×#63120⋊C3, AGL(1,𝔽5)×C13⋊C3×C49, #50303406, …
maximal normal subgroup ofC49×#63120⋊C3, AGL(1,𝔽5)×C13⋊C3×C49, #50303406, …
maximal quotient ofDic5×C13⋊C3×C49, C2×D5×C13⋊C3×C49

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 33);