Finite Group Databasebeta

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C3×C5×D799 #37561786

order23970
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D799
unambiguous semidirect productC17⋊(C3×C5×D47)
unambiguous semidirect productC47⋊(C3×C5×D17)

Splittings

Fitting, socle, HallC3×C5×C17×C47 ⋊ C2
derived, HallC17×C47 ⋊ C2×C3×C5
HallC5×C17×C47 ⋊ C2×C3
HallC3×C17×C47 ⋊ C2×C5
HallC3×C5×C47 ⋊ D17
HallC3×C5×C17 ⋊ D47
HallC5×C47 ⋊ C3×D17
HallC3×C47 ⋊ C5×D17
HallC5×C17 ⋊ C3×D47
HallC3×C17 ⋊ C5×D47
SylowC47 ⋊ C3×C5×D17
SylowC17 ⋊ C3×C5×D47

Subgroups

subgroupG/H
center, hypercenterC3×C5D799
commutator, cosocle, hypocenterC17×C47C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C47C2
LCSG ▷ C17×C47
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11985

Conjugacy classes & character table

6015 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23970, 4);