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C5×D21×D47 #34089503

order19740
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D21×D47
unambiguous semidirect product(C3×D47)⋊(C5×D7)
unambiguous semidirect product(C7×D47)⋊(C5×D3)

Splittings

Fitting, socle, HallC3×C5×C7×C47 ⋊ C22
derived, HallC3×C7×C47 ⋊ C22×C5
HallC5×C7×C47 ⋊ C2×D3
HallC3×C5×C47 ⋊ C2×D7
HallC7×C47 ⋊ C2×C5×D3
HallC5×C47 ⋊ C2×D21
HallC3×C47 ⋊ C2×C5×D7
HallC3×C5×C7 ⋊ C2×D47
SylowC47 ⋊ C2×C5×D21
HallC5×C7 ⋊ D3×D47
HallC3×C7 ⋊ C2×C5×D47
HallC3×C5 ⋊ D7×D47
SylowC7 ⋊ C5×D3×D47
SylowC3 ⋊ C5×D7×D47

Subgroups

subgroupG/H
center, hypercenterC5D21×D47
commutator, cosocle, hypocenterC3×C7×C47C22×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C47C22
LCSG ▷ C3×C7×C47
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4935

Conjugacy classes & character table

1500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 56);