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C3×C5×C5⋊(D13⋊C3) #19154353

order5850
isoclinismisoclinic class of C5⋊(D13⋊C3)
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C5⋊(D13⋊C3)
unambiguous semidirect productC5⋊(C3×C5×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C3×C5×D5)
unambiguous semidirect productD65⋊(C32×C5)
unambiguous semidirect product(C3×D65)⋊(C3×C5)
unambiguous semidirect product(C5×D65)⋊C32
unambiguous semidirect product(C3×C5×D65)⋊C3

Splittings

Fitting, socleC3×C52×C13 ⋊ C2×C3
derivedC5×C13 ⋊ C2×C32×C5
HallC3×C52×C13⋊C3 ⋊ C2
HallC5×D65 ⋊ C32
HallC52×C13 ⋊ C2×C32
HallC3×C13⋊C3 ⋊ C5×D5
SylowC52 ⋊ C3×D13⋊C3
SylowC13 ⋊ C32×C5×D5

Subgroups

subgroupG/H
center, hypercenterC3×C5C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C2×C32×C5
FrattiniC1G
Fitting, socleC3×C52×C13C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

330 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×#63122⋊C3, C3×C5×#63121⋊C3, C3×C5×D5×D13⋊C3, …
maximal normal subgroup ofC3×C5×#63122⋊C3, C3×C5×#63121⋊C3, C3×C5×D5×D13⋊C3, …
maximal quotient ofC3×C5×Dic65⋊C3, C2×C3×C5×C5⋊(D13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 69);