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C5×C13×D147 #34062022

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

Aliases

direct productC5×C13×D147
unambiguous semidirect productC3⋊(C5×C13×D49)
unambiguous semidirect productC49⋊(C5×D3×C13)

Splittings

Fitting, HallC3×C5×C13×C49 ⋊ C2
derived, HallC3×C49 ⋊ C2×C5×C13
HallC5×C13×C49 ⋊ D3
HallC3×C13×C49 ⋊ C2×C5
HallC3×C5×C49 ⋊ C2×C13
HallC13×C49 ⋊ C5×D3
HallC5×C49 ⋊ D3×C13
HallC3×C5×C13 ⋊ D49
SylowC49 ⋊ C5×D3×C13
HallC3×C13 ⋊ C5×D49
HallC3×C5 ⋊ C13×D49
SylowC3 ⋊ C5×C13×D49

Subgroups

subgroupG/H
center, hypercenterC5×C13D147
commutator, cosocle, hypocenterC3×C49C2×C5×C13
FrattiniC7C5×C13×D21
FittingC3×C5×C13×C49C2
socleC3×C5×C7×C13D7
LCSG ▷ C3×C49
UCSC1 ◁ C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

4875 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D13×D147, C5×D3×C13×D49, C5×D39⋊D49, …
maximal normal subgroup ofC5×D13×D147, C5×D3×C13×D49, C5×D39⋊D49, …
maximal quotient ofC5×C13×Dic147, C2×C5×C13×D147

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 15);