Finite Group Databasebeta

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C47×D255 #37561797

order23970
automorphism?
homologyAbelianization (H1) = C2×C47 · Schur multiplier (H2) = C1

Aliases

direct productC47×D255
unambiguous semidirect productC3⋊(C47×D85)
unambiguous semidirect productC5⋊(C47×D51)
unambiguous semidirect productC17⋊(D15×C47)

Splittings

Fitting, socle, HallC3×C5×C17×C47 ⋊ C2
derived, HallC3×C5×C17 ⋊ C2×C47
HallC5×C17×C47 ⋊ D3
HallC3×C17×C47 ⋊ D5
HallC17×C47 ⋊ D15
HallC3×C5×C47 ⋊ D17
HallC5×C47 ⋊ D51
HallC3×C47 ⋊ D85
HallC5×C17 ⋊ D3×C47
HallC3×C17 ⋊ D5×C47
SylowC17 ⋊ D15×C47
HallC3×C5 ⋊ D17×C47
SylowC5 ⋊ C47×D51
SylowC3 ⋊ C47×D85

Subgroups

subgroupG/H
center, hypercenterC47D255
commutator, cosocle, hypocenterC3×C5×C17C2×C47
FrattiniC1G
Fitting, socleC3×C5×C17×C47C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C47

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11985

Conjugacy classes & character table

6063 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23970, 15);