Finite Group Databasebeta

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C5×C47×C49⋊C3 #46828837

order34545
automorphism?
homologyAbelianization (H1) = C3×C5×C47 · Schur multiplier (H2) = C1

Aliases

direct productC5×C47×C49⋊C3
unambiguous semidirect productC49⋊(C3×C5×C47)
unambiguous semidirect product(C5×C49)⋊(C3×C47)
unambiguous semidirect product(C47×C49)⋊(C3×C5)
unambiguous semidirect product(C5×C47×C49)⋊C3

Splittings

Fitting, HallC5×C47×C49 ⋊ C3
derived, SylowC49 ⋊ C3×C5×C47
HallC47×C49 ⋊ C3×C5
HallC5×C49 ⋊ C3×C47

Subgroups

subgroupG/H
center, hypercenterC5×C47C49⋊C3
commutator, cosocle, hypocenterC49C3×C5×C47
FrattiniC7C5×ΓL(1,𝔽8)×C47
FittingC5×C47×C49C3
socleC5×C7×C47ΓL(1,𝔽8)
LCSG ▷ C49
UCSC1 ◁ C5×C47

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11515

Conjugacy classes & character table

4465 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34545, 2);