Finite Group Databasebeta

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C19×D15⋊D7 #22547736

order7980
isoclinismisoclinic class of D15⋊D7
automorphism?
homologyAbelianization (H1) = C22×C19 · Schur multiplier (H2) = C2

Aliases

direct productC19×D15⋊D7
unambiguous semidirect productD15⋊(D7×C19)
unambiguous semidirect productD21⋊(D5×C19)
unambiguous semidirect productD35⋊(D3×C19)

Splittings

Fitting, socle, HallC3×C5×C7×C19 ⋊ C22
derived, HallC3×C5×C7 ⋊ C22×C19
HallC5×C7×C19 ⋊ C2×D3
HallC3×C7×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C2×D7
HallC7×C19 ⋊ D3×D5
HallC5×C19 ⋊ D3×D7
HallC3×C19 ⋊ D5×D7
HallC5×C7 ⋊ C2×D3×C19
HallC3×C7 ⋊ C2×D5×C19
HallC3×C5 ⋊ C2×D7×C19
SylowC7 ⋊ D3×D5×C19
SylowC5 ⋊ D3×D7×C19
SylowC3 ⋊ D5×D7×C19

Subgroups

subgroupG/H
center, hypercenterC19D15⋊D7
commutator, hypocenterC3×C5×C7C22×C19
FrattiniC1G
Fitting, socleC3×C5×C7×C19C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C19

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

741 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×D35⋊D9, C19×D15⋊AGL(1,𝔽7), D15⋊#11716325, …
maximal normal subgroup ofC19×D15⋊AGL(1,𝔽7), D15⋊#11716325, D15⋊#11716326, …
maximal quotient ofC19×D35⋊D9, C3×C19×D15⋊D7, C19×D21⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 161);