Finite Group Databasebeta

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C19×C3⋊#66772 #34084376

order19380
automorphism?
homologyAbelianization (H1) = C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C3⋊#66772
unambiguous semidirect productC3⋊(C19×#66772)

Splittings

Fitting, socle, HallC3×C5×C17×C19 ⋊ C4
derived, HallC3×C5×C17 ⋊ C4×C19
HallC5×C17×C19 ⋊ Dic3
HallC3×C17×C19 ⋊ Dic5
HallC17×C19 ⋊ Dic15
HallC3×C5×C19 ⋊ #595
HallC5×C19 ⋊ C3⋊#595
HallC5×C17 ⋊ Dic3×C19
HallC3×C19 ⋊ #66772
HallC3×C17 ⋊ C19×Dic5
SylowC17 ⋊ C19×Dic15
HallC3×C5 ⋊ C19×#595
SylowC5 ⋊ C19×C3⋊#595
SylowC3 ⋊ C19×#66772

Subgroups

subgroupG/H
center, hypercenterC19C3⋊#66772
commutator, hypocenterC3×C5×C17C4×C19
FrattiniC1G
Fitting, socleC3×C5×C17×C19C4
prime radicalC3×C5×C19×D17C2
cosocleC3×C5×D17C2×C19
LCSG ▷ C3×C5×C17
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4845

Conjugacy classes & character table

1482 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 88);