Finite Group Databasebeta

← Prev (#46851899) Next (#46851901) →

C2×C19⋊C3×C61⋊C5 #46851900

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

Aliases

direct productC2×C19⋊C3×C61⋊C5
unambiguous semidirect product(C2×C19)⋊(C3×C61⋊C5)
unambiguous semidirect product(C2×C19⋊C3×C61)⋊C5

Splittings

Fitting, socle, HallC2×C19×C61 ⋊ C3×C5
derived, HallC19×C61 ⋊ C2×C3×C5
HallC2×C19×C61⋊C5 ⋊ C3
HallC2×C19⋊C3×C61 ⋊ C5
HallC19×C61⋊C5 ⋊ C2×C3
HallC19⋊C3×C61 ⋊ C2×C5
HallC2×C61 ⋊ C5×C19⋊C3
SylowC61 ⋊ C2×C5×C19⋊C3
HallC2×C19 ⋊ C3×C61⋊C5
SylowC19 ⋊ C2×C3×C61⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C19⋊C3×C61⋊C5
commutator, cosocle, hypocenterC19×C61C2×C3×C5
FrattiniC1G
Fitting, socleC2×C19×C61C3×C5
LCSG ▷ C19×C61
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2318

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34770, 8);