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C5×C3⋊(C3⋊(D41⋊C5)) #32914396

order18450
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC5×C3⋊(C3⋊(D41⋊C5))
unambiguous semidirect productC3⋊(C5×C3⋊(D41⋊C5))
unambiguous semidirect product(C41⋊C5)⋊(C5×C3⋊D3)
unambiguous semidirect product(C3⋊D123)⋊C52
unambiguous semidirect product(C5×C3⋊D123)⋊C5

Splittings

Fitting, socleC32×C5×C41 ⋊ C2×C5
derived, HallC32×C41 ⋊ C2×C52
HallC32×C5×C41⋊C5 ⋊ C2
HallC5×C41⋊C5 ⋊ C3⋊D3
HallC3⋊D123 ⋊ C52
SylowC41 ⋊ C52×C3⋊D3
SylowC32 ⋊ C5×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C3⋊(D41⋊C5))
commutator, cosocle, hypocenterC32×C41C2×C52
FrattiniC1G
Fitting, socleC32×C5×C41C2×C5
LCSG ▷ C32×C41
UCSC1 ◁ C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1845

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#13093287⋊C5, #20301657⋊C5, C5×D3×C3⋊(D41⋊C5), …
maximal normal subgroup ofC5×#13093287⋊C5, #20301657⋊C5, C5×D3×C3⋊(D41⋊C5), …
maximal quotient ofC5×C3⋊(C3⋊(Dic41⋊C5)), C2×C5×C3⋊(C3⋊(D41⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18450, 65);