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C5×D1911 #34062023

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

Aliases

direct productC5×D1911
unambiguous semidirect productC3⋊(C5×D637)
unambiguous semidirect productC13⋊(C5×D147)
unambiguous semidirect productC49⋊(C5×D39)

Splittings

Fitting, HallC3×C5×C13×C49 ⋊ C2
derived, HallC3×C13×C49 ⋊ C2×C5
HallC5×C13×C49 ⋊ D3
HallC3×C5×C49 ⋊ D13
HallC13×C49 ⋊ C5×D3
HallC5×C49 ⋊ D39
HallC3×C5×C13 ⋊ D49
HallC3×C49 ⋊ C5×D13
HallC5×C13 ⋊ D147
SylowC49 ⋊ C5×D39
HallC3×C13 ⋊ C5×D49
HallC3×C5 ⋊ D637
SylowC13 ⋊ C5×D147
SylowC3 ⋊ C5×D637

Subgroups

subgroupG/H
center, hypercenterC5D1911
commutator, cosocle, hypocenterC3×C13×C49C2×C5
FrattiniC7C5×D273
FittingC3×C5×C13×C49C2
socleC3×C5×C7×C13D7
LCSG ▷ C3×C13×C49
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

4785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D13×D147, C5×D39×D49, C5×D3×D637, …
maximal normal subgroup ofC5×D13×D147, C5×D39×D49, C5×D3×D637, …
maximal quotient ofC5×Dic1911, C2×C5×D1911

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 16);