Finite Group Databasebeta

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C5×D1947 #34085692

order19470
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1947
unambiguous semidirect productC3⋊(C5×D649)
unambiguous semidirect productC59⋊(C5×D33)

Splittings

Fitting, socle, HallC3×C5×C11×C59 ⋊ C2
derived, HallC3×C11×C59 ⋊ C2×C5
HallC5×C11×C59 ⋊ D3
HallC3×C5×C59 ⋊ D11
HallC11×C59 ⋊ C5×D3
HallC5×C59 ⋊ D33
HallC3×C59 ⋊ C5×D11
HallC3×C5×C11 ⋊ D59
SylowC59 ⋊ C5×D33
HallC5×C11 ⋊ D177
HallC3×C11 ⋊ C5×D59
HallC3×C5 ⋊ D649
SylowC11 ⋊ C5×D177
SylowC3 ⋊ C5×D649

Subgroups

subgroupG/H
center, hypercenterC5D1947
commutator, cosocle, hypocenterC3×C11×C59C2×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C59C2
LCSG ▷ C3×C11×C59
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9735

Conjugacy classes & character table

4875 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19470, 13);