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C52×C3⋊(D37⋊C3) #30659293

order16650
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×C3⋊(D37⋊C3)
unambiguous semidirect productC3⋊(C52×D37⋊C3)
unambiguous semidirect product(C37⋊C3)⋊(C52×D3)
unambiguous semidirect productD111⋊(C3×C52)
unambiguous semidirect product(C5×D111)⋊(C3×C5)

Splittings

Fitting, socleC3×C52×C37 ⋊ C2×C3
derivedC3×C37 ⋊ C2×C3×C52
HallC3×C52×C37⋊C3 ⋊ C2
HallC52×C37 ⋊ C3×D3
HallC3×C37⋊C3 ⋊ C2×C52
SylowC37 ⋊ C3×C52×D3

Subgroups

subgroupG/H
center, hypercenterC52C3⋊(D37⋊C3)
commutator, cosocle, hypocenterC3×C37C2×C3×C52
FrattiniC1G
Fitting, socleC3×C52×C37C2×C3
LCSG ▷ C3×C37
UCSC1 ◁ C52

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2775

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC52×D3×D37⋊C3, C5×D5×C3⋊(D37⋊C3), C5×D15⋊(D37⋊C3), …
maximal normal subgroup ofC52×D3×D37⋊C3, C5×D5×C3⋊(D37⋊C3), C5×D15⋊(D37⋊C3), …
maximal quotient ofC52×C3⋊(Dic37⋊C3), C2×C52×C3⋊(D37⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16650, 95);