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C3×C5⋊(C5⋊(D37⋊C3)) #30659283

order16650
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C5⋊(C5⋊(D37⋊C3))
unambiguous semidirect productC5⋊(C3×C5⋊(D37⋊C3))
unambiguous semidirect product(C37⋊C3)⋊(C3×C5⋊D5)

Splittings

Fitting, socleC3×C52×C37 ⋊ C2×C3
derived, HallC52×C37 ⋊ C2×C32
HallC3×C52×C37⋊C3 ⋊ C2
HallC5⋊D185 ⋊ C32
HallC3×C37⋊C3 ⋊ C5⋊D5
SylowC37 ⋊ C32×C5⋊D5
SylowC52 ⋊ C3×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(C5⋊(D37⋊C3))
commutator, cosocle, hypocenterC52×C37C2×C32
FrattiniC1G
Fitting, socleC3×C52×C37C2×C3
LCSG ▷ C52×C37
UCSC1 ◁ C3

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2775

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D5×C5⋊(D37⋊C3), C3×C5⋊D5×D37⋊C3, C3×#26012816, …
maximal normal subgroup ofC3×D5×C5⋊(D37⋊C3), C3×C5⋊D5×D37⋊C3, C3×#26012816, …
maximal quotient ofC3×#26012784, C2×C3×C5⋊(C5⋊(D37⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16650, 85);