Finite Group Databasebeta

← Prev (#18012326) Next (#18012328) →

C3×C7×C22⋊(C19⋊C3) #18012327

order4788
isoclinismisoclinic class of C22⋊(C19⋊C3)
automorphism?
homologyAbelianization (H1) = C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C7×C22⋊(C19⋊C3)
unambiguous semidirect product(C22×C3)⋊(C7×C19⋊C3)
unambiguous semidirect product(C3×C19)⋊(C7×A4)

Splittings

Fitting, socleC22×C3×C7×C19 ⋊ C3
derived, HallC22×C19 ⋊ C32×C7
HallC22×C7×C19 ⋊ C32
HallC7×C19 ⋊ C3×A4
HallC22×C7 ⋊ C3×C19⋊C3
SylowC19 ⋊ C3×C7×A4
SylowC22 ⋊ C3×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C7C22⋊(C19⋊C3)
commutator, cosocle, hypocenterC22×C19C32×C7
FrattiniC1G
Fitting, socleC22×C3×C7×C19C3
LCSG ▷ C22×C19
UCSC1 ◁ C3×C7

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1596

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C5×C7×C22⋊(C19⋊C3), C3×C49×C22⋊(C19⋊C3), C7×ΓL(1,𝔽8)×C22⋊(C19⋊C3), …
maximal normal subgroup ofC3×C5×C7×C22⋊(C19⋊C3), C3×C49×C22⋊(C19⋊C3), C3×C72×C22⋊(C19⋊C3)
maximal quotient ofC3×C5×C7×C22⋊(C19⋊C3), C3×C49×C22⋊(C19⋊C3), C7×ΓL(1,𝔽8)×C22⋊(C19⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 243);