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C47×D345 #44569869

order32430
automorphism?
homologyAbelianization (H1) = C2×C47 · Schur multiplier (H2) = C1

Aliases

direct productC47×D345
unambiguous semidirect productC3⋊(C47×D115)
unambiguous semidirect productC5⋊(C47×D69)
unambiguous semidirect productC23⋊(D15×C47)

Splittings

Fitting, socle, HallC3×C5×C23×C47 ⋊ C2
derived, HallC3×C5×C23 ⋊ C2×C47
HallC5×C23×C47 ⋊ D3
HallC3×C23×C47 ⋊ D5
HallC23×C47 ⋊ D15
HallC3×C5×C47 ⋊ D23
HallC5×C47 ⋊ D69
HallC3×C47 ⋊ D115
HallC5×C23 ⋊ D3×C47
HallC3×C23 ⋊ D5×C47
SylowC23 ⋊ D15×C47
HallC3×C5 ⋊ D23×C47
SylowC5 ⋊ C47×D69
SylowC3 ⋊ C47×D115

Subgroups

subgroupG/H
center, hypercenterC47D345
commutator, cosocle, hypocenterC3×C5×C23C2×C47
FrattiniC1G
Fitting, socleC3×C5×C23×C47C2
LCSG ▷ C3×C5×C23
UCSC1 ◁ C47

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16215

Conjugacy classes & character table

8178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32430, 16);