Finite Group Databasebeta

← Prev (#32916009) Next (#32916011) →

C2×C5×D19×C49 #32916010

order18620
automorphism?
homologyAbelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D19×C49
unambiguous semidirect productC19⋊(C22×C5×C49)
unambiguous semidirect product(C2×C19)⋊(C2×C5×C49)

Splittings

FittingC2×C5×C19×C49 ⋊ C2
derived, SylowC19 ⋊ C22×C5×C49
HallC5×C19×C49 ⋊ C22
HallC19×C49 ⋊ C22×C5
HallC5×C19 ⋊ C22×C49

Subgroups

subgroupG/H
center, hypercenterC2×C5×C49D19
commutator, hypocenterC19C22×C5×C49
FrattiniC7C2×C5×C7×D19
FittingC2×C5×C19×C49C2
socleC2×C5×C7×C19C2×C7
prime radicalC2×C5×C7×D19C7
cosocleC7×C19C22×C5×C7
LCSG ▷ C19
UCSC1 ◁ C2×C5×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9310

Conjugacy classes & character table

5390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18620, 27);