Finite Group Databasebeta

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C3⋊(C5⋊(C11⋊(D37⋊C3))) #49143758

order36630
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C5⋊(C11⋊(D37⋊C3)))
unambiguous semidirect productC5⋊(C3⋊(C11⋊(D37⋊C3)))
unambiguous semidirect productC11⋊(C3⋊(C5⋊(D37⋊C3)))
unambiguous semidirect product(C37⋊C3)⋊D165
unambiguous semidirect productD6105⋊C3

Splittings

Fitting, socle, derivedC3×C5×C11×C37 ⋊ C2×C3
HallC3×C5×C11×C37⋊C3 ⋊ C2
HallC3×C11×C37⋊C3 ⋊ D5
HallC5×C11×C37 ⋊ C3×D3
HallC3×C5×C37⋊C3 ⋊ D11
HallC11×C37 ⋊ C3×D15
HallC3×C37⋊C3 ⋊ D55
HallC5×C37 ⋊ C3×D33
HallC5×C11 ⋊ C3⋊(D37⋊C3)
SylowC37 ⋊ C3×D165
SylowC11 ⋊ C3⋊(C5⋊(D37⋊C3))
SylowC5 ⋊ C3⋊(C11⋊(D37⋊C3))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C37C2×C3
LCSG ▷ C3×C5×C11×C37
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Polycyclic presentation:

2,3^2,5,11,37|c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^36,f^b=f^26

Conjugacy classes & character table

1242 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36630, 82);