Finite Group Databasebeta

← Prev (#31825325) Next (#31825327) →

C3×C4×C5×C43⋊C7 #31825326

order18060
isoclinismisoclinic class of C43⋊C7
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C5×C43⋊C7
unambiguous semidirect product(C3×C4×C43)⋊(C5×C7)
unambiguous semidirect product(C3×C4×C5×C43)⋊C7

Splittings

Fitting, HallC3×C4×C5×C43 ⋊ C7
derived, SylowC43 ⋊ C3×C4×C5×C7
HallC4×C5×C43 ⋊ C3×C7
HallC3×C5×C43 ⋊ C4×C7
HallC3×C4×C43 ⋊ C5×C7
HallC5×C43 ⋊ C3×C4×C7
HallC4×C43 ⋊ C3×C5×C7
HallC3×C43 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5C43⋊C7
commutator, hypocenterC43C3×C4×C5×C7
FrattiniC2C2×C3×C5×C43⋊C7
FittingC3×C4×C5×C43C7
socleC2×C3×C5×C43C2×C7
prime radicalC2×C3×C5×C43⋊C7C2
cosocleC2×C43C2×C3×C5×C7
LCSG ▷ C43
UCSC1 ◁ C3×C4×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2580

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 2);