Finite Group Databasebeta

← Prev (#19154351) Next (#19154353) →

C3×C52×D13⋊C3 #19154352

order5850
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C52×D13⋊C3
unambiguous semidirect productD13⋊(C32×C52)
unambiguous semidirect product(C13⋊C3)⋊(C2×C3×C52)
unambiguous semidirect product(C3×D13)⋊(C3×C52)
unambiguous semidirect product(C5×D13)⋊(C32×C5)
unambiguous semidirect product(C3×C5×D13)⋊(C3×C5)

Splittings

Fitting, socleC3×C52×C13 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C32×C52
HallC3×C52×C13⋊C3 ⋊ C2
HallC52×D13 ⋊ C32
HallC52×C13 ⋊ C2×C32
HallC3×C13⋊C3 ⋊ C2×C52
HallD13 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC3×C52D13⋊C3
commutator, hypocenterC13C2×C32×C52
FrattiniC1G
Fitting, socleC3×C52×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C3×C52

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

600 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C52×AGL(1,𝔽13), C3×C5×#63118⋊C3, C3×C5×D5×D13⋊C3, …
maximal normal subgroup ofC3×C52×AGL(1,𝔽13), C3×C5×#63118⋊C3, C3×C5×D5×D13⋊C3, …
maximal quotient ofC3×C52×Dic13⋊C3, C2×C3×C52×D13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 68);