Finite Group Databasebeta

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C5×D3×C11×C37⋊C3 #49143753

order36630
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3×C11×C37⋊C3
unambiguous semidirect productC3⋊(C2×C5×C11×C37⋊C3)
unambiguous semidirect product(D3×C37)⋊(C3×C5×C11)
unambiguous semidirect product(C5×D3×C37)⋊(C3×C11)
unambiguous semidirect product(C5×D3×C11×C37)⋊C3

Splittings

Fitting, socleC3×C5×C11×C37 ⋊ C2×C3
derivedC3×C37 ⋊ C2×C3×C5×C11
HallC3×C5×C11×C37⋊C3 ⋊ C2
HallC3×C11×C37⋊C3 ⋊ C2×C5
HallC5×C11×C37 ⋊ C3×D3
HallC3×C5×C37⋊C3 ⋊ C2×C11
HallC11×C37 ⋊ C3×C5×D3
HallC3×C37⋊C3 ⋊ C2×C5×C11
HallC5×C37 ⋊ C3×D3×C11
SylowC37 ⋊ C3×C5×D3×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11D3×C37⋊C3
commutator, cosocle, hypocenterC3×C37C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C37C2×C3
LCSG ▷ C3×C37
UCSC1 ◁ C5×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

2475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36630, 77);