Finite Group Databasebeta

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C3×C19×#66772 #34084352

order19380
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19×#66772

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C19#66772
commutator, hypocenterC5×C17C3×C4×C19
FrattiniC1G
Fitting, socleC3×C5×C17×C19C4
prime radicalC3×C5×C19×D17C2
cosocleC5×D17C2×C3×C19
LCSG ▷ C5×C17
UCSC1 ◁ C3×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4845

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 64);