Finite Group Databasebeta

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C13×C3⋊(C3⋊(C5⋊D5)) #19154399

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

Aliases

direct productC13×C3⋊(C3⋊(C5⋊D5))
unambiguous semidirect productC3⋊(C13×C3⋊(C5⋊D5))
unambiguous semidirect productC5⋊(C13×C3⋊D15)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC13C3⋊(C3⋊(C5⋊D5))
commutator, hypocenterC32×C52C2×C13
FrattiniC1G
Fitting, socleC32×C52×C13C2
LCSG ▷ C32×C52
UCSC1 ◁ C13

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1482 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD13×C3⋊(C3⋊(C5⋊D5)), C13×C3⋊D3×C5⋊D5, #26043804, …
maximal normal subgroup ofD13×C3⋊(C3⋊(C5⋊D5)), C13×C3⋊D3×C5⋊D5, #26043804, …
maximal quotient ofC13×C3⋊(C3⋊#1039), C2×C13×C3⋊(C3⋊(C5⋊D5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 115);