Finite Group Databasebeta

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C3×C5×C7×D37⋊C3 #37552063

order23310
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C7×D37⋊C3
unambiguous semidirect productD37⋊(C32×C5×C7)
unambiguous semidirect product(C37⋊C3)⋊(C2×C3×C5×C7)
unambiguous semidirect product(C3×D37)⋊(C3×C5×C7)
unambiguous semidirect product(C5×D37)⋊(C32×C7)
unambiguous semidirect product(C3×C5×D37)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C2×C32×C5×C7
HallC3×C5×C7×C37⋊C3 ⋊ C2
HallC5×C7×D37 ⋊ C32
HallC3×C7×C37⋊C3 ⋊ C2×C5
HallC3×C5×C37⋊C3 ⋊ C2×C7
HallC5×C7×C37 ⋊ C2×C32
HallC7×D37 ⋊ C32×C5
HallC5×D37 ⋊ C32×C7
HallC3×C37⋊C3 ⋊ C2×C5×C7
HallC7×C37 ⋊ C2×C32×C5
HallC5×C37 ⋊ C2×C32×C7
HallD37 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7D37⋊C3
commutator, cosocle, hypocenterC37C2×C32×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C3×C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3885

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 82);