Finite Group Databasebeta

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C3×C19⋊#66775 #34084346

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

Aliases

direct productC3×C19⋊#66775

Splittings

Fitting, socle, HallC3×C5×C17×C19 ⋊ C4
derived, HallC5×C17×C19 ⋊ C3×C4
HallC3×C17×C19 ⋊ AGL(1,𝔽5)
HallC17×C19 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C19 ⋊ #595
HallC3×C5×C17 ⋊ Dic19
HallC5×C19 ⋊ C3×#595
HallC5×C17 ⋊ C3×Dic19
HallC3×C19 ⋊ #66775
HallC3×C17 ⋊ C19⋊AGL(1,𝔽5)
SylowC19 ⋊ C3×#66775
SylowC17 ⋊ C3×C19⋊AGL(1,𝔽5)
HallC3×C5 ⋊ C19⋊#595
SylowC5 ⋊ C3×C19⋊#595

Subgroups

subgroupG/H
center, hypercenterC3C19⋊#66775
commutator, hypocenterC5×C17×C19C3×C4
FrattiniC1G
Fitting, socleC3×C5×C17×C19C4
prime radicalC3×C19×D85C2
cosocleC19×D85C2×C3
LCSG ▷ C5×C17×C19
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4845

Conjugacy classes & character table

1263 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 58);