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C37×(C5⋊D5)⋊C9 #30659243

order16650
isoclinismisoclinic class of (C5⋊D5)⋊C3
automorphism?
homologyAbelianization (H1) = C2×C9×C37 · Schur multiplier (H2) = C5

Aliases

direct productC37×(C5⋊D5)⋊C9
unambiguous semidirect product(C5⋊D5)⋊(C9×C37)

Splittings

derived, SylowC52 ⋊ C2×C9×C37
HallC37×C52⋊C9 ⋊ C2
HallC37×C5⋊D5 ⋊ C9
HallC52×C37 ⋊ C2×C9
HallC52⋊C9 ⋊ C2×C37
HallC5⋊D5 ⋊ C9×C37

Subgroups

subgroupG/H
center, hypercenterC3×C37(C5⋊D5)⋊C3
commutator, hypocenterC52C2×C9×C37
FrattiniC3C37×(C5⋊D5)⋊C3
Fitting, socleC3×C52×C37C2×C3
prime radicalC3×C37×C5⋊D5C3
cosocleC3×C52C2×C3×C37
LCSG ▷ C52
UCSC1 ◁ C3×C37

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1665

Conjugacy classes & character table

1110 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC37×#90646⋊C2, ((C5⋊D5)⋊C9)⋊D37, C37×#1043⋊C9, …
maximal normal subgroup ofC37×#90646⋊C2, ((C5⋊D5)⋊C9)⋊D37, C37×#1043⋊C9, …
maximal quotient ofC37×#1039⋊C9, C2×C37×(C5⋊D5)⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16650, 45);