Finite Group Databasebeta

← Prev (#30659252) Next (#30659254) →

C5×C9×D5×C37 #30659253

order16650
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C37 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D5×C37
unambiguous semidirect productC5⋊(C2×C5×C9×C37)

Splittings

Fitting, HallC52×C9×C37 ⋊ C2
derivedC5 ⋊ C2×C5×C9×C37
HallC52×C37 ⋊ C2×C9
HallC52×C9 ⋊ C2×C37
SylowC52 ⋊ C2×C9×C37

Subgroups

subgroupG/H
center, hypercenterC5×C9×C37D5
commutator, hypocenterC5C2×C5×C9×C37
FrattiniC3C3×C5×D5×C37
FittingC52×C9×C37C2
socleC3×C52×C37C2×C3
prime radicalC3×C5×D5×C37C3
cosocleC3×C5C2×C3×C5×C37
LCSG ▷ C5
UCSC1 ◁ C5×C9×C37

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3330

Conjugacy classes & character table

6660 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×AGL(1,𝔽5)×C37, C5×C9×#10625193, C5×C9×D5×D37, …
maximal normal subgroup ofC5×C9×AGL(1,𝔽5)×C37, C5×C9×#10625193, C5×C9×D5×D37, …
maximal quotient ofC5×C9×Dic5×C37, C2×C5×C9×D5×C37

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16650, 55);