Finite Group Databasebeta

← Prev (#49153174) Next (#49153176) →

C3×D5×D623 #49153175

order37380
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×D623
unambiguous semidirect product(D5×C89)⋊(C3×D7)

Splittings

Fitting, socle, HallC3×C5×C7×C89 ⋊ C22
derived, HallC5×C7×C89 ⋊ C22×C3
HallC3×C7×C89 ⋊ C2×D5
HallC3×C5×C89 ⋊ C2×D7
HallC7×C89 ⋊ C2×C3×D5
HallC5×C89 ⋊ C2×C3×D7
HallC3×C89 ⋊ D5×D7
HallC3×C5×C7 ⋊ C2×D89
SylowC89 ⋊ C3×D5×D7
HallC5×C7 ⋊ C2×C3×D89
HallC3×C7 ⋊ D5×D89
HallC3×C5 ⋊ C2×D623
SylowC7 ⋊ C3×D5×D89
SylowC5 ⋊ C2×C3×D623

Subgroups

subgroupG/H
center, hypercenterC3D5×D623
commutator, cosocle, hypocenterC5×C7×C89C22×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C89C22
LCSG ▷ C5×C7×C89
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9345

Conjugacy classes & character table

3756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 69);