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C19×C3⋊#66775 #34084369

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

Aliases

direct productC19×C3⋊#66775
unambiguous semidirect productC3⋊(C19×#66775)

Splittings

Fitting, socle, HallC3×C5×C17×C19 ⋊ C4
derived, HallC3×C5×C17 ⋊ C4×C19
HallC5×C17×C19 ⋊ Dic3
HallC3×C17×C19 ⋊ AGL(1,𝔽5)
HallC17×C19 ⋊ ΓL(1,𝔽16)
HallC3×C5×C19 ⋊ #595
HallC5×C19 ⋊ C3⋊#595
HallC5×C17 ⋊ Dic3×C19
HallC3×C19 ⋊ #66775
HallC3×C17 ⋊ C19×AGL(1,𝔽5)
SylowC17 ⋊ C19×ΓL(1,𝔽16)
HallC3×C5 ⋊ C19×#595
SylowC5 ⋊ C19×C3⋊#595
SylowC3 ⋊ C19×#66775

Subgroups

subgroupG/H
center, hypercenterC19C3⋊#66775
commutator, hypocenterC3×C5×C17C4×C19
FrattiniC1G
Fitting, socleC3×C5×C17×C19C4
prime radicalC3×C19×D85C2
cosocleC3×D85C2×C19
LCSG ▷ C3×C5×C17
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4845

Conjugacy classes & character table

1311 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 81);