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C5×D15×C37⋊C3 #30659296

order16650
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D15×C37⋊C3
unambiguous semidirect productC3⋊(C5×D5×C37⋊C3)
unambiguous semidirect productC5⋊(C5×D3×C37⋊C3)
unambiguous semidirect product(D15×C37)⋊(C3×C5)
unambiguous semidirect product(C5×D15×C37)⋊C3

Splittings

Fitting, socleC3×C52×C37 ⋊ C2×C3
derivedC3×C5×C37 ⋊ C2×C3×C5
HallC3×C52×C37⋊C3 ⋊ C2
HallC52×C37 ⋊ C3×D3
HallC3×C37⋊C3 ⋊ C5×D5
SylowC37 ⋊ C3×C5×D15
SylowC52 ⋊ D3×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D15×C37⋊C3
commutator, cosocle, hypocenterC3×C5×C37C2×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C37C2×C3
LCSG ▷ C3×C5×C37
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1110

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D15×D37⋊C3, C5×D15⋊(D37⋊C3), C5×D3×D5×C37⋊C3, …
maximal normal subgroup ofC5×D15×D37⋊C3, C5×D15⋊(D37⋊C3), C5×D3×D5×C37⋊C3, …
maximal quotient ofC5×Dic15×C37⋊C3, C2×C5×D15×C37⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16650, 98);