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C3×C5×C7×A4×C13 #30655774

order16380
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C5×C7×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×C7×A4×C13
unambiguous semidirect productC22⋊(C32×C5×C7×C13)
unambiguous semidirect product(C22×C3)⋊(C3×C5×C7×C13)
unambiguous semidirect product(C22×C5)⋊(C32×C7×C13)
unambiguous semidirect product(C22×C3×C5)⋊(C3×C7×C13)

Splittings

Fitting, socleC22×C3×C5×C7×C13 ⋊ C3
derived, SylowC22 ⋊ C32×C5×C7×C13
HallC22×C5×C7×C13 ⋊ C32
HallC22×C7×C13 ⋊ C32×C5
HallC22×C5×C13 ⋊ C32×C7
HallC22×C5×C7 ⋊ C32×C13
HallC22×C13 ⋊ C32×C5×C7
HallC22×C7 ⋊ C32×C5×C13
HallC22×C5 ⋊ C32×C7×C13

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7×C13A4
commutator, cosocle, hypocenterC22C32×C5×C7×C13
FrattiniC1G
Fitting, socleC22×C3×C5×C7×C13C3
LCSG ▷ C22
UCSC1 ◁ C3×C5×C7×C13

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

5460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 824);