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C3×C13×C3⋊(C5⋊D5) #19154393

order5850
isoclinismisoclinic class of C3⋊(C5⋊D5)
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C5

Aliases

direct productC3×C13×C3⋊(C5⋊D5)
unambiguous semidirect productC3⋊(C3×C13×C5⋊D5)
unambiguous semidirect productC5⋊(C3×C13×D15)

Splittings

Fitting, socle, HallC32×C52×C13 ⋊ C2
derivedC3×C52 ⋊ C2×C3×C13
HallC52×C13 ⋊ C3×D3
HallC32×C52 ⋊ C2×C13
HallC32×C13 ⋊ C5⋊D5
SylowC52 ⋊ C3×D3×C13
SylowC32 ⋊ C13×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC3×C13C3⋊(C5⋊D5)
commutator, hypocenterC3×C52C2×C3×C13
FrattiniC1G
Fitting, socleC32×C52×C13C2
LCSG ▷ C3×C52
UCSC1 ◁ C3×C13

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1521 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D13×C3⋊(C5⋊D5), C3×D3×C13×C5⋊D5, C3×D39⋊(C5⋊D5), …
maximal normal subgroup ofC3×D13×C3⋊(C5⋊D5), C3×D3×C13×C5⋊D5, C3×D39⋊(C5⋊D5), …
maximal quotient ofC3×C13×C3⋊#1039, C2×C3×C13×C3⋊(C5⋊D5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 109);