Finite Group Databasebeta

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C2×C19×D255 #34084403

order19380
automorphism?
homologyAbelianization (H1) = C22×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C19×D255
unambiguous semidirect product(C2×C3)⋊(C19×D85)
unambiguous semidirect product(C2×C5)⋊(C19×D51)
unambiguous semidirect product(C2×C17)⋊(C19×D15)

Splittings

Fitting, socleC2×C3×C5×C17×C19 ⋊ C2
derived, HallC3×C5×C17 ⋊ C22×C19
HallC3×C5×C17×C19 ⋊ C22
HallC5×C17×C19 ⋊ C2×D3
HallC3×C17×C19 ⋊ C2×D5
HallC17×C19 ⋊ C2×D15
HallC3×C5×C19 ⋊ C2×D17
HallC5×C19 ⋊ C2×D51
HallC5×C17 ⋊ C2×D3×C19
HallC3×C19 ⋊ C2×D85
HallC3×C17 ⋊ C2×D5×C19
SylowC17 ⋊ C2×C19×D15
HallC3×C5 ⋊ C2×C19×D17
SylowC5 ⋊ C2×C19×D51
SylowC3 ⋊ C2×C19×D85

Subgroups

subgroupG/H
center, hypercenterC2×C19D255
commutator, cosocle, hypocenterC3×C5×C17C22×C19
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C19C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C2×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9690

Conjugacy classes & character table

4902 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 115);