Finite Group Databasebeta

← Prev (#26046178) Next (#26046180) →

C3×C5⋊((C19⋊C3)⋊D7) #26046179

order11970
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5⋊((C19⋊C3)⋊D7)
unambiguous semidirect productC5⋊(C3×(C19⋊C3)⋊D7)
unambiguous semidirect product(C19⋊C3)⋊(C3×D35)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C2×C3
derived, HallC5×C7×C19 ⋊ C2×C32
HallC3×C5×C7×C19⋊C3 ⋊ C2
HallD665 ⋊ C32
HallC3×C7×C19⋊C3 ⋊ D5
HallC3×C5×C19⋊C3 ⋊ D7
HallC3×C19⋊C3 ⋊ D35
HallC7×C19 ⋊ C32×D5
HallC5×C19 ⋊ C32×D7
HallC5×C7 ⋊ C3×D19⋊C3
SylowC19 ⋊ C32×D35
SylowC7 ⋊ C3×C5⋊(D19⋊C3)
SylowC5 ⋊ C3×(C19⋊C3)⋊D7

Subgroups

subgroupG/H
center, hypercenterC3C5⋊((C19⋊C3)⋊D7)
commutator, cosocle, hypocenterC5×C7×C19C2×C32
FrattiniC1G
Fitting, socleC3×C5×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

486 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D35×D19⋊C3, C3×D7×C5⋊(D19⋊C3), C3×D5×(C19⋊C3)⋊D7, …
maximal normal subgroup ofC3×D35×D19⋊C3, C3×D7×C5⋊(D19⋊C3), C3×D5×(C19⋊C3)⋊D7, …
maximal quotient ofC3×(C19⋊C3)⋊Dic35, C2×C3×C5⋊((C19⋊C3)⋊D7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 108);