Finite Group Databasebeta

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C3×C19⋊(D61⋊C5) #46851920

order34770
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19⋊(D61⋊C5)
unambiguous semidirect product(C3×D1159)⋊C5

Splittings

Fitting, socle, HallC3×C19×C61 ⋊ C2×C5
derived, HallC19×C61 ⋊ C2×C3×C5
HallC3×C19×C61⋊C5 ⋊ C2
HallC3×D1159 ⋊ C5
HallC19×C61⋊C5 ⋊ C2×C3
HallD1159 ⋊ C3×C5
HallC3×C61⋊C5 ⋊ D19
HallC61⋊C5 ⋊ C3×D19
HallC3×C61 ⋊ C5×D19
SylowC61 ⋊ C3×C5×D19
HallC3×C19 ⋊ D61⋊C5
SylowC19 ⋊ C3×D61⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C19⋊(D61⋊C5)
commutator, cosocle, hypocenterC19×C61C2×C3×C5
FrattiniC1G
Fitting, socleC3×C19×C61C2×C5
LCSG ▷ C19×C61
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3477

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34770, 28);