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C17×C19×ΓL(1,𝔽16) #34084367

order19380
automorphism?
homologyAbelianization (H1) = C4×C17×C19 · Schur multiplier (H2) = C1

Aliases

direct productC17×C19×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C17×C19×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C17×C19 ⋊ C4
derived, HallC3×C5 ⋊ C4×C17×C19
HallC5×C17×C19 ⋊ Dic3
HallC3×C17×C19 ⋊ AGL(1,𝔽5)
HallC3×C5×C19 ⋊ C4×C17
HallC3×C5×C17 ⋊ C4×C19
HallC5×C19 ⋊ Dic3×C17
HallC5×C17 ⋊ Dic3×C19
HallC3×C19 ⋊ C17×AGL(1,𝔽5)
HallC3×C17 ⋊ C19×AGL(1,𝔽5)
SylowC5 ⋊ Dic3×C17×C19
SylowC3 ⋊ C17×C19×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC17×C19ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C17×C19
FrattiniC1G
Fitting, socleC3×C5×C17×C19C4
prime radicalC3×D5×C17×C19C2
cosocleC3×D5C2×C17×C19
LCSG ▷ C3×C5
UCSC1 ◁ C17×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4845

Conjugacy classes & character table

2907 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 79);