Finite Group Databasebeta

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C37×C3⋊#66772 #49179878

order37740
automorphism?
homologyAbelianization (H1) = C4×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×C3⋊#66772
unambiguous semidirect productC3⋊(C37×#66772)

Splittings

Fitting, socle, HallC3×C5×C17×C37 ⋊ C4
derived, HallC3×C5×C17 ⋊ C4×C37
HallC5×C17×C37 ⋊ Dic3
HallC3×C17×C37 ⋊ Dic5
HallC17×C37 ⋊ Dic15
HallC3×C5×C37 ⋊ #595
HallC5×C37 ⋊ C3⋊#595
HallC3×C37 ⋊ #66772
HallC5×C17 ⋊ Dic3×C37
HallC3×C17 ⋊ Dic5×C37
SylowC17 ⋊ C37×Dic15
HallC3×C5 ⋊ C37×#595
SylowC5 ⋊ C37×C3⋊#595
SylowC3 ⋊ C37×#66772

Subgroups

subgroupG/H
center, hypercenterC37C3⋊#66772
commutator, hypocenterC3×C5×C17C4×C37
FrattiniC1G
Fitting, socleC3×C5×C17×C37C4
prime radicalC3×C5×D17×C37C2
cosocleC3×C5×D17C2×C37
LCSG ▷ C3×C5×C17
UCSC1 ◁ C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9435

Conjugacy classes & character table

2886 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37740, 133);