Finite Group Databasebeta

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C19×C3⋊D255 #44414697

order29070
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C3

Aliases

direct productC19×C3⋊D255
unambiguous semidirect productC3⋊(C19×D255)
unambiguous semidirect productC5⋊(C19×C3⋊D51)
unambiguous semidirect productC17⋊(C19×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C17×C19 ⋊ C2
derived, HallC32×C5×C17 ⋊ C2×C19
HallC32×C17×C19 ⋊ D5
HallC5×C17×C19 ⋊ C3⋊D3
HallC32×C5×C19 ⋊ D17
HallC17×C19 ⋊ C3⋊D15
HallC32×C19 ⋊ D85
HallC32×C17 ⋊ D5×C19
HallC5×C19 ⋊ C3⋊D51
HallC5×C17 ⋊ C3⋊D3×C19
HallC32×C5 ⋊ C19×D17
SylowC17 ⋊ C19×C3⋊D15
SylowC32 ⋊ C19×D85
SylowC5 ⋊ C19×C3⋊D51

Subgroups

subgroupG/H
center, hypercenterC19C3⋊D255
commutator, cosocle, hypocenterC32×C5×C17C2×C19
FrattiniC1G
Fitting, socleC32×C5×C17×C19C2
LCSG ▷ C32×C5×C17
UCSC1 ◁ C19

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14535

Conjugacy classes & character table

7296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29070, 71);