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C5×C3⋊(C5⋊(D13⋊C3)) #19154367

order5850
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C5⋊(D13⋊C3))
unambiguous semidirect productC3⋊(C5×C5⋊(D13⋊C3))
unambiguous semidirect productC5⋊(C5×C3⋊(D13⋊C3))
unambiguous semidirect product(C13⋊C3)⋊(C5×D15)
unambiguous semidirect productD195⋊(C3×C5)
unambiguous semidirect product(C5×D195)⋊C3

Splittings

Fitting, socleC3×C52×C13 ⋊ C2×C3
derivedC3×C5×C13 ⋊ C2×C3×C5
HallC3×C52×C13⋊C3 ⋊ C2
HallC52×C13 ⋊ C3×D3
HallC3×C13⋊C3 ⋊ C5×D5
SylowC52 ⋊ C3⋊(D13⋊C3)
SylowC13 ⋊ C3×C5×D15

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C5⋊(D13⋊C3))
commutator, hypocenterC3×C5×C13C2×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C13C2×C3
LCSG ▷ C3×C5×C13
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

285 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D15×D13⋊C3, C5×D5×C3⋊(D13⋊C3), C5×D3×C5⋊(D13⋊C3), …
maximal normal subgroup ofC5×D15×D13⋊C3, C5×D5×C3⋊(D13⋊C3), C5×D3×C5⋊(D13⋊C3), …
maximal quotient ofC5×C3⋊(Dic65⋊C3), C2×C5×C3⋊(C5⋊(D13⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 83);