Finite Group Databasebeta

← Prev (#37561791) Next (#37561793) →

C5×C17×D141 #37561792

order23970
automorphism?
homologyAbelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×D141
unambiguous semidirect productC3⋊(C5×C17×D47)
unambiguous semidirect productC47⋊(C5×D3×C17)

Splittings

Fitting, socle, HallC3×C5×C17×C47 ⋊ C2
derived, HallC3×C47 ⋊ C2×C5×C17
HallC5×C17×C47 ⋊ D3
HallC3×C17×C47 ⋊ C2×C5
HallC17×C47 ⋊ C5×D3
HallC3×C5×C47 ⋊ C2×C17
HallC3×C5×C17 ⋊ D47
HallC5×C47 ⋊ D3×C17
HallC3×C17 ⋊ C5×D47
SylowC47 ⋊ C5×D3×C17
HallC3×C5 ⋊ C17×D47
SylowC3 ⋊ C5×C17×D47

Subgroups

subgroupG/H
center, hypercenterC5×C17D141
commutator, cosocle, hypocenterC3×C47C2×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C47C2
LCSG ▷ C3×C47
UCSC1 ◁ C5×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11985

Conjugacy classes & character table

6120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23970, 10);