Finite Group Databasebeta

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C3×D5×C13×C49 #34062016

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C13×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5×C13×C49
unambiguous semidirect productC5⋊(C2×C3×C13×C49)

Splittings

Fitting, HallC3×C5×C13×C49 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C13×C49
HallC5×C13×C49 ⋊ C2×C3
HallC3×C5×C49 ⋊ C2×C13
HallC5×C49 ⋊ C2×C3×C13
HallC3×C5×C13 ⋊ C2×C49
HallC5×C13 ⋊ C2×C3×C49
HallC3×C5 ⋊ C2×C13×C49

Subgroups

subgroupG/H
center, hypercenterC3×C13×C49D5
commutator, hypocenterC5C2×C3×C13×C49
FrattiniC7C3×C7×D5×C13
FittingC3×C5×C13×C49C2
socleC3×C5×C7×C13C2×C7
prime radicalC3×C7×D5×C13C7
cosocleC5×C7C2×C3×C7×C13
LCSG ▷ C5
UCSC1 ◁ C3×C13×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

7644 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C13×AGL(1,𝔽5)×C49, C3×C49×#63120, C3×C13×C49⋊AGL(1,𝔽5), …
maximal normal subgroup ofC3×C13×AGL(1,𝔽5)×C49, C3×C49×#63120, C3×C13×C49⋊AGL(1,𝔽5), …
maximal quotient ofC3×C13×Dic5×C49, C2×C3×D5×C13×C49

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 9);