Finite Group Databasebeta

← Prev (#19154364) Next (#19154366) →

C52×C3⋊(D13⋊C3) #19154365

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

Aliases

direct productC52×C3⋊(D13⋊C3)
unambiguous semidirect productC3⋊(C52×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C52×D3)
unambiguous semidirect productD39⋊(C3×C52)
unambiguous semidirect product(C5×D39)⋊(C3×C5)

Splittings

Fitting, socleC3×C52×C13 ⋊ C2×C3
derivedC3×C13 ⋊ C2×C3×C52
HallC3×C52×C13⋊C3 ⋊ C2
HallC52×C13 ⋊ C3×D3
HallC3×C13⋊C3 ⋊ C2×C52
SylowC13 ⋊ C3×C52×D3

Subgroups

subgroupG/H
center, hypercenterC52C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C2×C3×C52
FrattiniC1G
Fitting, socleC3×C52×C13C2×C3
LCSG ▷ C3×C13
UCSC1 ◁ C52

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

375 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC52×D3×D13⋊C3, C5×D5×C3⋊(D13⋊C3), C5×D15⋊(D13⋊C3), …
maximal normal subgroup ofC52×D3×D13⋊C3, C5×D5×C3⋊(D13⋊C3), C5×D15⋊(D13⋊C3), …
maximal quotient ofC52×C3⋊(Dic13⋊C3), C2×C52×C3⋊(D13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 81);