Finite Group Databasebeta

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C3×C5×D17×D23 #37553293

order23460
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C5×D17×D23
unambiguous semidirect product(C23×D17)⋊(C2×C3×C5)
unambiguous semidirect product(C17×D23)⋊(C2×C3×C5)
unambiguous semidirect productD391⋊(C2×C3×C5)

Splittings

Fitting, socle, HallC3×C5×C17×C23 ⋊ C22
derived, HallC17×C23 ⋊ C22×C3×C5
HallC5×C17×C23 ⋊ C22×C3
HallC3×C17×C23 ⋊ C22×C5
HallC3×C5×C23 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D23
HallC5×C23 ⋊ C2×C3×D17
HallC5×C17 ⋊ C2×C3×D23
HallC3×C23 ⋊ C2×C5×D17
HallC3×C17 ⋊ C2×C5×D23
SylowC23 ⋊ C2×C3×C5×D17
SylowC17 ⋊ C2×C3×C5×D23

Subgroups

subgroupG/H
center, hypercenterC3×C5D17×D23
commutator, cosocle, hypocenterC17×C23C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C23C22
LCSG ▷ C17×C23
UCSC1 ◁ C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5865

Conjugacy classes & character table

1950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 20);