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D5×C29×C37⋊C3 #44565728

order32190
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productD5×C29×C37⋊C3
unambiguous semidirect productC5⋊(C2×C29×C37⋊C3)
unambiguous semidirect product(D5×C37)⋊(C3×C29)
unambiguous semidirect product(D5×C29×C37)⋊C3

Splittings

Fitting, socle, HallC5×C29×C37 ⋊ C2×C3
derived, HallC5×C37 ⋊ C2×C3×C29
HallC5×C29×C37⋊C3 ⋊ C2
HallD5×C29×C37 ⋊ C3
HallC29×C37 ⋊ C3×D5
HallC5×C37⋊C3 ⋊ C2×C29
HallD5×C37 ⋊ C3×C29
HallC5×C29 ⋊ C2×C37⋊C3
SylowC37 ⋊ C3×D5×C29
SylowC5 ⋊ C2×C29×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC29D5×C37⋊C3
commutator, cosocle, hypocenterC5×C37C2×C3×C29
FrattiniC1G
Fitting, socleC5×C29×C37C2×C3
LCSG ▷ C5×C37
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5365

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32190, 21);